Covers Unit 11 (Plane figures, lines, symmetry & shapes) and Unit 12 (Measuring angles & additive angles).
Open Study Guide: Free review reference with worked examples and check-yourself problems. Note: Achieving 90% mastery of Units 11 & 12 on Khan Academy beforehand is strongly recommended to prepare for test scoring.
Unit 11 — Plane Figures & Symmetry
Concept 1
Lines, Rays, and Angles
Core Vocabulary:
Point: An exact position in space (dot).
Line: Goes on forever in both directions (arrows on both ends ↔).
Line Segment: Part of a line between two distinct endpoints (•—•).
Ray: Has one endpoint and continues forever in one direction (•→).
Parallel Lines: Never meet, stay equal distance apart.
Perpendicular Lines: Intersect at an exact 90° right angle.
Understanding:
Concept 2
Classifying Triangles and Quadrilaterals
Triangles by Angle:
Right Triangle: Exactly one 90° right angle.
Acute Triangle: All 3 angles are acute (< 90°).
Obtuse Triangle: Exactly one obtuse angle (> 90°).
Quadrilaterals:
Trapezoid: Exactly one pair of parallel sides (standard CCSS definition).
Parallelogram: 2 pairs of parallel sides.
Rhombus: Parallelogram with 4 equal sides.
Rectangle: Parallelogram with 4 right angles.
Square: 4 equal sides AND 4 right angles (both a rhombus and a rectangle!).
Understanding:
Concept 3
Lines of Symmetry
The Fold Test: A line of symmetry divides a shape into two mirror-image halves that match up perfectly when folded along the line.
Worked Example: Counting Lines of Symmetry
• Square: 4 lines of symmetry (horizontal, vertical, 2 diagonals).
• Rectangle: 2 lines of symmetry (horizontal and vertical; diagonals do NOT fold evenly!).
• Equilateral Triangle: 3 lines of symmetry.
• Scalene Triangle: 0 lines of symmetry.
Understanding:
Unit 12 — Measuring Angles
Concept 4
Angle Types and Protractor Reading
Angle Degrees: A full circle is 360°. A straight line is 180°. A right angle is 90°.
Acute: Between 0° and 90°.
Right: Exactly 90° (square corner symbol).
Obtuse: Between 90° and 180°.
Protractor Double Scale Tip: Protractors have two sets of numbers (inside and outside). Look at the angle: if it is acute, choose the number < 90°! If it is obtuse, choose the number > 90°!
Understanding:
Concept 5
Adjacent Angles & Angle Addition
Additive Rule: When an angle is split into smaller adjacent parts, the sum of the parts equals the whole angle: ∠Total = ∠Part 1 + ∠Part 2.
Worked Example: Decomposing a 130° Angle
A 130° angle is split into two angles. One angle measures 45°.
What is the other angle? 130° − 45° = 85°.
Understanding:
Concept 6
Right Angles (90°) and Straight Lines (180°)
Two Classic Benchmarks:
Right Angle Benchmark: Two angles forming a right angle always add to 90°: ∠A + ∠B = 90°.
Straight Line Benchmark: Two angles on a straight line always add to 180°: ∠A + ∠B = 180°.
Worked Example: Straight Line Angles
An angle on a straight line is 65°. What is the missing adjacent angle? 180° − 65° = 115°.