Geometry and Geometric Measurement
The Geometry and Geometric Measurement domain tests lines, line segments, rays, angles, parallel and perpendicular lines, classification of two-dimensional figures, lines of symmetry, and angle measurement. Questions often combine naming a figure with measuring or reasoning about its angles.
Lines, rays, and angles
- A line extends in both directions without endpoints. A line segment has two endpoints. A ray has one endpoint and extends in one direction.
- An angle is formed by two rays that share a vertex. Angle size is measured in degrees and does not depend on the lengths of the rays.
- A right angle measures 90°, an acute angle is less than 90°, and an obtuse angle is greater than 90° but less than 180°. A straight angle measures 180°.
- Parallel lines never meet and stay the same distance apart. Perpendicular lines meet at a right angle.
Classifying figures
- Triangles can be classified by sides: equilateral (three equal sides), isosceles (at least two equal sides), and scalene (no equal sides). They can also be classified by angles: acute, right, or obtuse.
- Quadrilaterals include trapezoids, parallelograms, rectangles, rhombuses, and squares. A square is also a rectangle, a rhombus, and a parallelogram because it satisfies each definition.
- A line of symmetry divides a figure into two matching halves that fold onto each other.
Angle measurement
- Place the protractor center on the vertex and align one ray with the zero mark. Read the scale that starts at zero on that ray.
- Adjacent angles that form a right angle add to 90°. Adjacent angles that form a straight angle add to 180°.
Worked example
Two adjacent angles form a right angle. One angle measures 37°. Find the other angle. A right angle is 90°, so subtract: 90° − 37° = 53°. The second angle measures 53°, and 37° + 53° = 90° checks the result.
Traps that cost marks
- Judging an angle by the length of its rays rather than by the opening between them.
- Reading the wrong protractor scale, especially when the ray does not point to zero on the outer scale.
- Calling a square only a square and not recognizing it as a rectangle and rhombus.
- Confusing a line, ray, and segment when naming a figure.
- Assuming every quadrilateral has a line of symmetry or that every triangle is equilateral.