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Castilla-La Mancha PAU Technical Drawing II (Dibujo Técnico II - UCLM 2026) study materials
Castilla-La Mancha PAU Technical Drawing II (Dibujo Técnico II - UCLM 2026) study resources

Castilla-La Mancha PAU Technical Drawing II (Dibujo Técnico II - UCLM 2026) practice questions

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Question 1Technical drawing: plane and spatial geometry, projections and dimensions

What is the intersection point of the three perpendicular bisectors of the sides of a triangle called?

  1. Circumcenter. Correct answer.
  2. Incenter.
  3. Orthocenter.
  4. Centroid.

Explanation

The circumcenter is the point where the three perpendicular bisectors of the sides of a triangle intersect, and it is the center of the circumscribed circle (circumcircle).

Question 2Technical drawing: plane and spatial geometry, projections and dimensions

What geometric property characterizes the points belonging to an arc of a constant angle α (arc capable of angle α) subtended by a segment AB?

  1. The sum of the distances from any point on the arc to A and B is constant.
  2. From any point on the arc, segment AB is viewed under the same angle α. Correct answer.
  3. The product of the distances from any point on the arc to A and B is constant.
  4. From any point on the arc, segment AB is viewed under an angle of 90° - α.

Explanation

By definition, the arc of a constant angle α (arc capable) for a segment AB is the locus of points from which segment AB is subtended under a constant angle α.

Question 3Technical drawing: plane and spatial geometry, projections and dimensions

In a plane homology transformation defined by center O, axis e, and a pair of homologous points A and A', what happens to two parallel lines r and s?

  1. They always transform into two parallel lines.
  2. Their homologous lines r' and s' intersect at a point located on the vanishing line (línea límite). Correct answer.
  3. They transform into two concentric circles.
  4. Their homologous lines intersect at a point located on axis e.

Explanation

In plane homology, parallel lines intersect at a point at infinity, whose homologous image is a point on the vanishing line. Therefore, their homologous lines intersect at that point on the vanishing line.

Question 4Technical drawing: plane and spatial geometry, projections and dimensions

In a plane homothety with center O and scale factor k = -2, how does the resulting figure compare to the original figure?

  1. It is smaller and maintains the same orientation.
  2. It is twice as large, rotated 90°, and inverted.
  3. It is twice as large and inverted (rotated 180°) with respect to the center O. Correct answer.
  4. It preserves the exact same size and orientation.

Explanation

Since the scale factor k is negative (|k| = 2), distances are multiplied by 2 and homologous points lie on opposite sides of center O, resulting in an inverted figure (rotated 180°).

Question 5Technical drawing: plane and spatial geometry, projections and dimensions

What is the radical axis of two non-concentric circles?

  1. The locus of points in the plane that have equal power with respect to both circles. Correct answer.
  2. The straight line connecting the centers of both circles.
  3. A circle whose radius is the geometric mean of the radii of both circles.
  4. The straight line that divides both circles into regions of equal area.

Explanation

The radical axis is defined as the locus of points in the plane having equal power with respect to two given circles. It is always a straight line perpendicular to the line connecting their centers.

Question 6Technical drawing: plane and spatial geometry, projections and dimensions

How many radical axes intersect to determine the radical center of three non-collinear circles?

  1. One.
  2. Three radical axes that concur at a single point. Correct answer.
  3. Four radical axes.
  4. Two exterior tangent lines.

Explanation

The three radical axes formed by considering the circles in pairs concur at a single point known as the radical center.

Question 7Technical drawing: plane and spatial geometry, projections and dimensions

What is the definition of the locus of points that forms an ellipse?

  1. Points whose difference of distances to two fixed points (foci) is constant.
  2. Points whose distance to a fixed point (focus) equals their distance to a fixed line (directrix).
  3. Points whose sum of distances to two fixed points (foci) is constant and equal to 2a. Correct answer.
  4. Points whose product of distances to two foci is a given constant.

Explanation

An ellipse is the locus of points P in the plane such that the sum of their distances to two fixed points F and F' (foci) is constant and equal to the length of the major axis (2a).

Question 8Technical drawing: plane and spatial geometry, projections and dimensions

What is the eccentricity e of a parabola?

  1. e = 0.
  2. 0 < e < 1.
  3. e = 1. Correct answer.
  4. e > 1.

Explanation

By the focal definition of a conic, the eccentricity of a parabola is exactly e = 1, since any point on it is equidistant from the focus and the directrix (d(P,F)/d(P,d) = 1).

Question 9Technical drawing: plane and spatial geometry, projections and dimensions

In dividing a segment AB in extreme and mean ratio (golden section), what is the approximate numerical value of the golden ratio Φ?

  1. 1.414.
  2. 1.732.
  3. 2.718.
  4. 1.618. Correct answer.

Explanation

The golden ratio is mathematically expressed as Φ = (1 + √5) / 2 ≈ 1.61803398...

Question 10Technical drawing: plane and spatial geometry, projections and dimensions

In any triangle, the sum of interior angles is 180°. How are the orthocenter and circumcenter located in an obtuse triangle?

  1. Both points lie outside the triangle. Correct answer.
  2. The orthocenter lies inside and the circumcenter lies outside.
  3. The circumcenter lies on the hypotenuse and the orthocenter at the vertex of the obtuse angle.
  4. Both points lie exactly at the midpoint of the longest side.

Explanation

In an obtuse triangle, both the orthocenter and the circumcenter lie outside the region of the triangle: the circumcenter lies outside facing the obtuse angle, and the orthocenter lies outside behind the vertex of the obtuse angle.

Question 11Technical drawing: plane and spatial geometry, projections and dimensions

What is the relation between the focal distance 2c, the major axis 2a, and the minor axis 2b in an ellipse?

  1. a² = b² + c². Correct answer.
  2. b² = a² + c².
  3. c² = a² + b².
  4. a = b + c.

Explanation

In an ellipse, the semi-major axis a forms the hypotenuse of the right triangle whose legs are the semi-minor axis b and the semi-focal distance c, so a² = b² + c².

Question 12Technical drawing: plane and spatial geometry, projections and dimensions

What is the focal circumference (circunferencia focal) of an ellipse?

  1. The circle centered at the origin of coordinates with radius a.
  2. The circle centered at one of the foci with radius equal to the major axis 2a. Correct answer.
  3. The circle whose diameter is equal to the minor axis 2b.
  4. The circle passing through all four vertices of the ellipse.

Explanation

In an ellipse, each focal circumference is centered at one focus (F or F') and has a radius equal to the major axis length 2a. It is the locus of symmetric points of the other focus with respect to all tangent lines.

Question 13Technical drawing: plane and spatial geometry, projections and dimensions

What is the principal circle (circunferencia principal) of an ellipse or hyperbola?

  1. The locus of the feet of the perpendiculars dropped from the foci onto any tangent to the curve. Correct answer.
  2. The circle passing through both foci.
  3. The circle centered at a focus with radius 2a.
  4. The circle circumscribing the focal rectangle.

Explanation

The principal circle is centered at the center of the conic with radius a (the semi-major axis). It is defined as the locus of the feet of the perpendiculars drawn from the foci to any tangent line.

Question 14Technical drawing: plane and spatial geometry, projections and dimensions

What are the asymptotes of a hyperbola?

  1. Two lines tangent to the hyperbola at its vertices.
  2. Two lines passing through the center of the hyperbola to which the curve approaches indefinitely without ever touching it (tangents at infinity). Correct answer.
  3. The axes of symmetry of the hyperbola.
  4. Two lines perpendicular to the major axis passing through the foci.

Explanation

The asymptotes of a hyperbola are two lines passing through its center that act as tangents to the curve at infinity.

Question 15Technical drawing: plane and spatial geometry, projections and dimensions

In an inversion transformation in the plane with center O and positive power K > 0, what is the inverse image of a circle that does not pass through the center of inversion O?

  1. A straight line not passing through O.
  2. Another circle that also does not pass through O. Correct answer.
  3. A parabola.
  4. A straight line passing through O.

Explanation

In plane inversion, any circle that does not pass through the center of inversion O transforms into another circle that also does not pass through O.

Question 16Technical drawing: plane and spatial geometry, projections and dimensions

What is the inverse image of a straight line that passes through the center of inversion O?

  1. A circle passing through O.
  2. The same straight line (line invariant as a whole). Correct answer.
  3. A circle not passing through O.
  4. A point.

Explanation

Any straight line passing through the center of inversion O is transformed into itself (invariant as a whole line), although individual points swap positions according to OP · OP' = K.

Question 17Technical drawing: plane and spatial geometry, projections and dimensions

How are the slopes of the asymptotes of a hyperbola centered at the origin with equation x²/a² - y²/b² = 1 calculated?

  1. m = ± a / b.
  2. m = ± b / a. Correct answer.
  3. m = ± c / a.
  4. m = ± b / c.

Explanation

The equations of the asymptotes of a hyperbola centered at the origin are y = ± (b/a)x, so their slopes are m = ± b/a.

Question 18Technical drawing: plane and spatial geometry, projections and dimensions

What is the locus of the symmetric points of the focus F with respect to all tangents to a parabola?

  1. The principal circle.
  2. The axis of symmetry of the parabola.
  3. The directrix of the parabola. Correct answer.
  4. The vertex of the parabola.

Explanation

In a parabola, the symmetric points of the focus F with respect to any tangent line to the curve lie on its directrix (which acts as a focal circle of infinite radius).

Question 19Technical drawing: plane and spatial geometry, projections and dimensions

What is the interior angle of a regular convex decagon?

  1. 108°.
  2. 120°.
  3. 135°.
  4. 144°. Correct answer.

Explanation

The interior angle of a regular polygon of n sides is given by α = 180° · (n - 2) / n. For n = 10: α = 180° · 8 / 10 = 144°.

Question 20Technical drawing: plane and spatial geometry, projections and dimensions

In a plane homology defined by center O, axis e, and a pair of homologous points A and A', what condition is satisfied by all lines connecting homologous points B and B'?

  1. They are all parallel to axis e.
  2. All lines connecting homologous points (BB', CC') concur at the center of homology O. Correct answer.
  3. They always form a constant angle of 45° with axis e.
  4. They intersect on the vanishing line l of the homology.

Explanation

By definition of plane homology, the lines connecting pairs of homologous points concur at a single point called the center of homology O.

Question 21Technical drawing: plane and spatial geometry, projections and dimensions

What is the main characteristic of a plane affinity compared to general plane homology?

  1. The center of homology O is located at infinity, so the lines connecting homologous points are parallel to one another. Correct answer.
  2. The axis of affinity does not exist.
  3. It does not preserve parallelism between lines.
  4. Affine figures are invariably congruent (identical).

Explanation

Plane affinity is a special case of homology whose center O is at infinity (affinity direction), implying that all lines connecting affine points are parallel to each other and parallelism between lines is preserved.

Question 22Technical drawing: plane and spatial geometry, projections and dimensions

When applying an inversion transformation to solve a tangency problem between three circles (Apollonius' CCC case), what advantage is gained by choosing the center of inversion O at an intersection point of two of them?

  1. The three circles transform into points.
  2. The two circles passing through O transform into two straight lines, reducing the problem to the Line-Line-Circle (LLC) case. Correct answer.
  3. The problem simplifies to the bisector of three points.
  4. The third circle transforms into a straight line parallel to the line of centers.

Explanation

Choosing the center of inversion O at a common point of two circles transforms those two circles into straight lines, radically simplifying the problem to the tangency case of two lines and a circle.

Question 23Technical drawing: plane and spatial geometry, projections and dimensions

In an ellipse, what are two conjugate diameters?

  1. Any two mutually perpendicular diameters.
  2. Two diameters of equal length that intersect at a focus.
  3. Two diameters such that each bisects all chords parallel to the other. Correct answer.
  4. Two segments connecting the center to the foci.

Explanation

By definition, two diameters of an ellipse are conjugate when each bisects all chords parallel to the other diameter.

Question 24Technical drawing: plane and spatial geometry, projections and dimensions

How many tangent lines can be drawn to an ellipse from an exterior point P?

  1. A single tangent line.
  2. Exactly two tangent lines. Correct answer.
  3. Four tangent lines.
  4. Infinitely many tangent lines.

Explanation

From any point exterior to a second-degree conic (ellipse, hyperbola, or parabola), exactly two tangent lines can be drawn to the curve.

Question 25Technical drawing: plane and spatial geometry, projections and dimensions

According to Dandelin's Theorems, when a cone of revolution is intersected by a plane generating an ellipse, what do the contact points of the Dandelin spheres inscribed in the cone and tangent to the cutting plane represent?

  1. The vertices of the minor axis of the ellipse.
  2. The vertices of the major axis of the ellipse.
  3. The two foci F and F' of the section ellipse. Correct answer.
  4. The intersection points of the axis of the cone with the cutting plane.

Explanation

Dandelin's Theorem geometrically proves that the points of tangency between the cutting plane and the two spheres inscribed in the cone (tangent internally to the cone's mantle) are precisely the two foci F1 and F2 of the section ellipse.

Question 26Technical drawing: plane and spatial geometry, projections and dimensions

In double orthographic projection (dihedric system), what is the condition for a line r to be a horizontal line (level line)?

  1. Its vertical projection r' is parallel to the ground line (LT), and its horizontal projection r is inclined relative to LT. Correct answer.
  2. Its horizontal projection r is parallel to the ground line LT.
  3. Both projections r and r' are perpendicular to the ground line LT.
  4. It does not have a horizontal trace.

Explanation

A horizontal line (level line) is parallel to the horizontal plane of projection, so all its points have constant elevation (cota). Therefore, its vertical projection r' is parallel to the ground line LT, while its horizontal projection r shows true magnitude of length for horizontal segments.

Question 27Technical drawing: plane and spatial geometry, projections and dimensions

In the dihedric system, how is a frontal plane α (parallel to the Vertical Plane of Projection, VP) projected?

  1. It has no horizontal trace at finite distance (α is at infinity) and a vertical trace α' parallel to LT.
  2. It has a horizontal trace α perpendicular to LT and a vertical trace α' parallel to LT.
  3. Its horizontal trace α is parallel to LT and it has no vertical trace α'. Correct answer.
  4. Both its horizontal trace α and its vertical trace α' are parallel to LT.

Explanation

A frontal plane is parallel to the VP and perpendicular to the HP. Its intersection with the HP forms a horizontal trace α parallel to the ground line LT, and it does not intersect the VP at a finite distance (its vertical trace α' is at infinity).

Question 28Technical drawing: plane and spatial geometry, projections and dimensions

What position does a 'profile line' occupy relative to the main projection planes HP and VP in the dihedric system?

  1. It is parallel to both projection planes HP and VP.
  2. It is contained in or parallel to a profile plane (perpendicular to both HP and VP and perpendicular to the ground line). Correct answer.
  3. It is perpendicular to the horizontal projection plane HP.
  4. It is parallel to the bisector planes.

Explanation

A profile line belongs to or is parallel to a profile plane (perpendicular to both HP and VP). Its horizontal and vertical projections are both perpendicular to the ground line LT.

Question 29Technical drawing: plane and spatial geometry, projections and dimensions

How are the traces of two parallel planes α and β related to each other in the dihedric system?

  1. Their horizontal traces α and β are perpendicular, and their vertical traces α' and β' are parallel.
  2. Their homologous traces are parallel to each other: α || β and α' || β'. Correct answer.
  3. Their traces intersect on the ground line forming 45°.
  4. Their horizontal traces intersect, while their vertical traces are parallel.

Explanation

Two planes are parallel in space if and only if their respective homologous traces are parallel to each other: α || β on the horizontal plane and α' || β' on the vertical plane.

Question 30Technical drawing: plane and spatial geometry, projections and dimensions

When are two lines r and s parallel to each other in the dihedric system?

  1. When their horizontal projections are parallel (r || s) and their vertical projections are also parallel (r' || s') [except for profile lines, which require checking on a third projection]. Correct answer.
  2. When their projections cross at 90° in the drawing.
  3. When their vertical projections are parallel, regardless of their horizontal projections.
  4. When their traces coincide at the same point on the ground line.

Explanation

In general, two lines are parallel in space if their homonymous projections are parallel (r || s and r' || s'). For profile lines, an auxiliary profile view is required to confirm parallelism.

Question 31Technical drawing: plane and spatial geometry, projections and dimensions

How is the intersection point I between a general line r and a general plane α determined in the dihedric system?

  1. By passing an auxiliary plane β (usually a projecting plane) through line r, finding the intersection line i between planes α and β, and then finding the intersection point I between lines r and i. Correct answer.
  2. By measuring the distance from the horizontal trace of r to the vertical trace of α.
  3. By drawing a line perpendicular to LT from the intersection of the vertical projections.
  4. By rotating the line r until it becomes parallel to α.

Explanation

The standard method to find I = r ∩ α is: 1) Pass an auxiliary projecting plane β containing r; 2) Find the intersection line i = α ∩ β; 3) Find the intersection point I = r ∩ i.

Question 32Technical drawing: plane and spatial geometry, projections and dimensions

What condition is required for a line r to be perpendicular to a plane α in the dihedric system?

  1. That the horizontal projection of the line r is perpendicular to the horizontal trace α of the plane (r ⊥ α), and the vertical projection r' is perpendicular to the vertical trace α' (r' ⊥ α'). Correct answer.
  2. That their vertical projections form 45° with the ground line.
  3. That the line r is parallel to the ground line and α is a projecting plane.
  4. That the traces of the line intersect the traces of the plane at a single point.

Explanation

In orthographic projection, a line is perpendicular to a plane if and only if its horizontal projection is perpendicular to the plane's horizontal trace (r ⊥ α) and its vertical projection is perpendicular to the plane's vertical trace (r' ⊥ α').

Question 33Technical drawing: plane and spatial geometry, projections and dimensions

To obtain the true magnitude of an oblique segment AB in the dihedric system using the difference-of-elevations triangle method, what are the legs of the right triangle constructed?

  1. The horizontal projection ab of the segment, and the absolute difference of elevations (Δz = |z_A - z_B|) between its endpoints. Correct answer.
  2. The vertical projection a'b' and the sum of distances to the profile plane.
  3. Both projections ab and a'b' placed end-to-end.
  4. The ground line LT and the distance between traces.

Explanation

The true magnitude of segment AB is the hypotenuse of a right triangle whose legs are the horizontal projection ab and the elevation difference Δz = |z_A - z_B| (or alternatively, vertical projection a'b' and distance difference Δy).

Question 34Technical drawing: plane and spatial geometry, projections and dimensions

In the rebatment (abatment) of a plane α onto the Horizontal Plane of Projection (HP), which element of the plane acts as the axis of rotation (hinge / charnela)?

  1. The vertical trace α' of the plane.
  2. The horizontal trace α of the plane. Correct answer.
  3. The ground line LT.
  4. The profile trace of the plane.

Explanation

When rebatting (abatting) a plane onto the HP, the horizontal trace α of the plane remains in the HP and serves as the axis of rotation (charnela).

Question 35Technical drawing: plane and spatial geometry, projections and dimensions

What is a 'line of steepest slope' (recta de máxima pendiente) of a plane α in the dihedric system?

  1. A line contained in the plane α whose horizontal projection is perpendicular to the horizontal trace α of the plane. Correct answer.
  2. A line contained in the plane α whose vertical projection is perpendicular to the vertical trace α' of the plane.
  3. A line parallel to the ground line contained in α.
  4. A line contained in α forming 45° with both projection planes.

Explanation

A line of steepest slope of a plane α is a line in α that forms the maximum angle with the HP. Its horizontal projection is perpendicular to the horizontal trace α.

Question 36Technical drawing: plane and spatial geometry, projections and dimensions

What is the main characteristic of a horizontally projecting plane (vertical plane)?

  1. It is perpendicular to the Horizontal Plane of Projection (HP); all figures contained in it project onto its horizontal trace α. Correct answer.
  2. It is perpendicular to the Vertical Plane of Projection (VP).
  3. It is parallel to both projection planes.
  4. Its horizontal trace is parallel to the ground line.

Explanation

A horizontally projecting plane is perpendicular to HP. Its horizontal projection is an accumulating line (all points in the plane project onto its horizontal trace α).

Question 37Technical drawing: plane and spatial geometry, projections and dimensions

How is a 'plane parallel to the ground line' positioned in the dihedric system?

  1. Both of its traces α and α' are parallel to the ground line LT. Correct answer.
  2. Its horizontal trace α is perpendicular to LT and its vertical trace α' is parallel to LT.
  3. It has no horizontal trace α.
  4. Its traces intersect at the origin of coordinates.

Explanation

A plane parallel to LT has both its horizontal trace α and vertical trace α' parallel to the ground line LT.

Question 38Technical drawing: plane and spatial geometry, projections and dimensions

In a change of vertical projection plane in the dihedric system (replacing VP with a new VP1), which coordinate or measurement of the points remains INVARIANT?

  1. The distance to the profile plane (alejamientos).
  2. The elevation (cota / height z) of all points. Correct answer.
  3. The horizontal projection.
  4. The distance to the origin.

Explanation

When changing the vertical projection plane, the horizontal plane remains fixed, so the elevations (cota / height z) of all points remain completely unchanged.

Question 39Technical drawing: plane and spatial geometry, projections and dimensions

Where are the traces of a line r located if it lies entirely within the first bisector plane (β1)?

  1. Its horizontal trace H and vertical trace V coincide at the same point on the ground line LT. Correct answer.
  2. Its horizontal trace is at infinity and its vertical trace is on LT.
  3. It has no traces.
  4. Its traces are symmetric with respect to the origin.

Explanation

Since the first bisector plane β1 passes through the ground line LT, any line contained in β1 must intersect the projection planes on LT, so its traces H and V coincide on LT.

Question 40Technical drawing: plane and spatial geometry, projections and dimensions

In a regular tetrahedron of edge length a, what formula expresses its height h in terms of a?

  1. h = a √(2/3). Correct answer.
  2. h = a √3 / 2.
  3. h = a √2.
  4. h = a / 2.

Explanation

The height of a regular tetrahedron of edge a is derived from geometry as h = a √(2/3) = a √6 / 3.

Question 41Technical drawing: plane and spatial geometry, projections and dimensions

In a regular octahedron of edge length a, how many faces and vertices does this regular polyhedron have?

  1. 6 faces and 8 vertices.
  2. 8 faces and 6 vertices. Correct answer.
  3. 12 faces and 6 vertices.
  4. 8 faces and 12 vertices.

Explanation

A regular octahedron is composed of 8 equilateral triangular faces, 6 vertices, and 12 edges (satisfying Euler's formula V - E + F = 6 - 12 + 8 = 2).

Question 42Technical drawing: plane and spatial geometry, projections and dimensions

If the horizontal traces of two planes α and β are parallel to each other (α || β), what is the nature of the intersection line i between both planes?

  1. It is a vertical line.
  2. It is a horizontal line (level line) whose horizontal projection i is parallel to α and β. Correct answer.
  3. It is a line perpendicular to the ground line.
  4. The two planes never intersect.

Explanation

If two planes have parallel horizontal traces (α || β), their intersection line i is a horizontal line (level line). Its horizontal projection i is parallel to traces α and β, and its vertical projection i' is parallel to the ground line.

Question 43Technical drawing: plane and spatial geometry, projections and dimensions

To convert a general oblique line r into a horizontal line via a change of dihedric projection plane, where must the new ground line LT1 be placed?

  1. Parallel to the vertical projection r'.
  2. Parallel to the horizontal projection r. Correct answer.
  3. Perpendicular to the horizontal projection r.
  4. Forming 45° with the vertical projection r'.

Explanation

When performing a vertical plane change while maintaining the horizontal projection plane, the new ground line LT1 must be drawn parallel to the horizontal projection r so that the line becomes parallel to the new vertical projection plane (level/frontal line).

Question 44Technical drawing: plane and spatial geometry, projections and dimensions

To convert a general oblique plane α into a horizontally projecting plane via a change of projection plane, where must the new ground line LT1 be drawn?

  1. Parallel to the vertical trace α'.
  2. Perpendicular to the horizontal trace α. Correct answer.
  3. Parallel to the horizontal trace α.
  4. Coinciding with the first bisector plane.

Explanation

To convert plane α into a vertically projecting plane (plano de canto) using a new vertical plane, the new ground line LT1 must be drawn perpendicular to the horizontal trace α.

Question 45Technical drawing: plane and spatial geometry, projections and dimensions

When rotating a point P in space around a vertical axis e (perpendicular to HP), what trajectory does its vertical projection P' describe?

  1. A circular arc of radius r centered at e'.
  2. A straight line segment parallel to the ground line (maintaining constant elevation). Correct answer.
  3. Foreshortened ellipse.
  4. An unaltered fixed point.

Explanation

When rotating around a vertical axis, the elevation (cota) of point P remains strictly constant. Consequently, its vertical projection P' moves along a straight line segment parallel to the ground line.

Question 46Technical drawing: plane and spatial geometry, projections and dimensions

To find the true distance from a point P to a general oblique plane α, what is the correct dihedric procedure?

  1. 1. Draw a line r through P perpendicular to plane α. 2. Find the intersection point I of r with α. 3. Determine the true magnitude of segment PI. Correct answer.
  2. Measure the distance directly between projection P' and vertical trace α'.
  3. Rebat plane α and measure from P to the charnela.
  4. Draw a line parallel to the ground line through P and intersect α.

Explanation

The distance from a point to a plane is defined as the length of the segment perpendicular to the plane drawn from the point. The direct dihedric method consists of drawing r ⊥ α through P, finding intersection I = r ∩ α, and obtaining the true magnitude of PI.

Question 47Technical drawing: plane and spatial geometry, projections and dimensions

How is the minimum distance between two parallel lines r and s determined in the dihedric system?

  1. By adding the distance between their horizontal projections and vertical projections.
  2. By defining the plane α containing r and s, and finding the true magnitude of a perpendicular section drawn between them. Correct answer.
  3. By taking any point of r and projecting it perpendicularly onto the projection plane.
  4. By finding the intersection point of r and s with the first bisector plane.

Explanation

Two parallel lines r and s define a plane α. The distance between them is the length of the segment perpendicular to both contained in plane α, which is measured in true magnitude by rebatting α or making the lines point-projecting via a change of plane.

Question 48Technical drawing: plane and spatial geometry, projections and dimensions

How is the angle formed by an oblique line r with the Horizontal Plane of Projection (HP) obtained?

  1. Measure directly the angle between projection r and the ground line.
  2. By change of plane (converting r into a frontal line) or by the difference-of-elevations right triangle where horizontal projection r is set against elevation difference. Correct answer.
  3. Subtract 90° from the elevation of the highest point of r.
  4. Drawing the angle formed by r' with the Z axis.

Explanation

The angle of r with HP is the angle formed by the line in space with its horizontal projection r. In the difference-of-elevations right triangle (legs r and Δz), the angle adjacent to projection r is the true angle with HP.

Question 49Technical drawing: plane and spatial geometry, projections and dimensions

A regular hexahedron (cube) of edge length a rests on one of its faces on the Horizontal Plane of Projection. What is the length of its main space diagonal?

  1. d = a √2.
  2. d = a √3. Correct answer.
  3. d = a √5.
  4. d = 2a.

Explanation

The face diagonal of a cube of edge a is a√2. Applying the Pythagorean theorem again with the vertical edge gives d = √((a√2)² + a²) = √(2a² + a²) = a√3.

Question 50Technical drawing: plane and spatial geometry, projections and dimensions

What is the number of planes of symmetry possessed by a cube (regular hexahedron)?

  1. 3.
  2. 6.
  3. 9. Correct answer.
  4. 12.

Explanation

A cube has 9 planes of symmetry: 3 parallel to the faces (principal symmetry planes) and 6 passing through diagonally opposite edges (diagonal symmetry planes).