- 1. What an Angle Really Is — Turn, Parts, and Names
Describe an angle as an amount of turn between two rays that meet at a point, identify the vertex and arms, name an angle three ways, and explain why arm length does not change an angle.
- 2. Measuring the Turn — Degrees, the Protractor, and the Five Types of Angle
State that a full turn is 360 degrees, measure and draw angles with a protractor using the correct scale, and classify any angle as acute, right, obtuse, straight, or reflex.
- 3. Angles on a Straight Line Add to 180° — Supplementary Angles
State that angles on a straight line add up to 180 degrees, find a missing angle by subtracting from 180, define supplementary and complementary angles, and solve simple algebra problems on a line.
- 4. Angles Around a Point Add to 360°
State that angles around a point add to 360 degrees, find a missing angle by subtracting from 360, distinguish the 180-degree line rule from the 360-degree point rule, and solve algebra problems at a point.
- 5. When Two Lines Cross — Vertically Opposite Angles Are Equal
Identify the two pairs of vertically opposite angles at a crossing, use and explain why vertically opposite angles are equal, and find all four angles when one is known.
- 6. Parallel Lines and a Transversal — Corresponding Angles (the “F”)
Identify a transversal and corresponding angles on parallel lines, use the fact that corresponding angles are equal, and combine this with earlier angle facts.
- 7. Alternate Angles on Parallel Lines — the “Z”
Identify alternate angles between parallel lines, use the fact that they are equal, explain why by linking to corresponding and vertically opposite angles, and mix the parallel-line facts.
- 8. Co-interior Angles on Parallel Lines — the “C” — Add to 180°
Identify co-interior (allied) angles, use the fact that they add to 180 degrees, explain why using alternate and straight-line facts, and choose correctly between the F, Z, and C rules.
- 9. The Angles in a Triangle Add to 180°
State and use the fact that the three interior angles of a triangle add to 180 degrees, find a missing angle including with algebra, classify triangles, and understand why the sum is 180 using alternate angles.
- 10. Angle Sums of Quadrilaterals and Polygons — (n − 2) × 180°
Find the interior-angle sum of a quadrilateral and any polygon using (n-2) x 180, find a missing angle, find one interior angle of a regular polygon, and solve multi-step figures combining polygons, straight lines, and triangles.
