Geometry
What this domain covers
Geometry tests identifying and drawing points, lines, line segments, rays, and angles; recognizing parallel and perpendicular lines; classifying triangles and quadrilaterals by their properties; finding lines of symmetry; and solving angle problems.
Core rules to know
- Lines and rays: a line extends forever in both directions; a line segment has two endpoints; a ray has one endpoint and extends forever in one direction.
- Angle types: acute < 90°, right = 90°, obtuse > 90° and < 180°, straight = 180°.
- Parallel and perpendicular: parallel lines never meet and stay the same distance apart; perpendicular lines meet at a right angle.
- Classifying shapes: triangles can be right, acute, or obtuse, and equilateral, isosceles, or scalene. Quadrilaterals include parallelograms, rectangles, rhombuses, squares, and trapezoids, defined by parallel sides, equal sides, and right angles.
- Symmetry: a line of symmetry folds a figure onto itself. A square has 4; a non-square rectangle has 2.
Worked example
A straight angle is split into three angles. Two measure 65° and 40°. Find the third. A straight angle measures 180°. 65 + 40 = 105°. 180 − 105 = 75°. The three angles must add to 180° because they form a straight angle. Check: 65 + 40 + 75 = 180.
Traps that cost marks
- Calling a ray a line, or counting endpoints incorrectly.
- Assuming a shape is a square because it looks square; use given side and angle marks.
- Using 360° for a straight angle or 90° for any angle that looks small.
- Classifying a rhombus as a square without four right angles.
- Counting diagonal folds as lines of symmetry when the halves do not match.