Praxis Geometry flashcards
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32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Vertical angles
- Two nonadjacent angles formed by intersecting lines. They are always congruent, so setting their measures equal is a valid first step in angle problems.
- Linear pair
- Two adjacent angles whose noncommon sides form a straight line. Their measures add to 180 degrees, which lets you solve for an unknown angle.
- Alternate interior angles
- Angles on opposite sides of a transversal between two parallel lines. They are congruent, a key test for proving lines parallel.
- Corresponding angles
- Angles in matching positions at each intersection when a transversal crosses two lines. If the lines are parallel, these angles are congruent.
- Triangle angle sum theorem
- The three interior angles of any triangle add to 180 degrees. Use it to find a missing angle when the other two are known.
- Exterior angle theorem
- An exterior angle of a triangle equals the sum of the two remote interior angles. It also exceeds either remote interior angle individually.
- SSS congruence
- If three sides of one triangle match three sides of another, the triangles are congruent. No angle information is needed for this criterion.
- SAS congruence
- If two sides and the included angle of one triangle match those of another, the triangles are congruent. The angle must lie between the named sides.
- ASA congruence
- If two angles and the included side of one triangle match another's, the triangles are congruent. The side must lie between the named angles.
- AAS congruence
- If two angles and a nonincluded side of one triangle match another's, the triangles are congruent. It follows from ASA via the angle sum theorem.
- HL congruence
- If the hypotenuse and one leg of a right triangle match those of another right triangle, they are congruent. It applies only to right triangles.
- AA similarity
- If two angles of one triangle equal two angles of another, the triangles are similar. The third pair then follows from the angle sum.
- Scale factor and area
- For similar figures with linear scale factor k, perimeters scale by k and areas scale by k squared. Volumes of similar solids scale by k cubed.
- Pythagorean theorem
- In a right triangle, the sum of the squares of the legs equals the square of the hypotenuse: a squared plus b squared equals c squared.
- Pythagorean converse
- If the squares of two sides sum to the square of the longest side, the triangle is right. Greater sums mean acute; lesser sums mean obtuse.
- 45-45-90 triangle
- An isosceles right triangle whose legs are equal and whose hypotenuse equals a leg times the square root of 2. Side ratio is 1 to 1 to root 2.
- 30-60-90 triangle
- A right triangle with angles 30, 60, and 90 degrees. Sides are in ratio 1 to root 3 to 2, with the shortest side opposite the 30 degree angle.
- Inscribed angle theorem
- An angle inscribed in a circle measures half its intercepted arc. An angle inscribed in a semicircle is therefore a right angle.
- Tangent-radius theorem
- A tangent line is perpendicular to the radius drawn to the point of tangency. This creates a right triangle usable with the Pythagorean theorem.
- Chord-chord angle
- The angle formed by two chords meeting inside a circle equals half the sum of the arcs intercepted by it and its vertical angle.
- Secant angle outside circle
- An angle formed by two secants or tangents from an external point equals half the difference of the intercepted arcs, larger minus smaller.
- Central angle and arc
- A central angle has the same measure as its intercepted minor arc. Arc length equals the central angle over 360 times the circumference.
- Circle area and circumference
- Area equals pi times the radius squared; circumference equals 2 pi times the radius, or pi times the diameter. Both use the same radius value.
- Sector area
- A sector's area equals its central angle divided by 360, multiplied by pi times the radius squared. It is a fraction of the whole circle.
- Triangle area formula
- Area equals one half times base times height, where height is perpendicular to the chosen base. Any side can serve as the base.
- Trapezoid area formula
- Area equals one half times the sum of the parallel bases times the height. The height is the perpendicular distance between the bases.
- Regular polygon area
- Area equals one half times the apothem times the perimeter. The apothem is the perpendicular distance from center to a side.
- Prism and cylinder volume
- Volume equals base area times height. For a cylinder this becomes pi times radius squared times height, since the base is a circle.
- Pyramid and cone volume
- Volume equals one third times base area times height. A cone uses pi times radius squared as its base area.
- Sphere volume and surface area
- Volume equals four thirds pi times radius cubed; surface area equals 4 pi times radius squared. Both depend only on the radius.
- Coordinate distance formula
- The distance between two points equals the square root of the sum of squared differences in x and y. It is the Pythagorean theorem on the plane.
- Coordinate midpoint formula
- The midpoint of a segment averages the x-coordinates and averages the y-coordinates of its endpoints. Each coordinate is the mean of the pair.