Year 7 Maths • AC9M7M04 • Homework
Parallel Lines, Transversals and Angle Relationships
Identify the angle relationship first, then calculate and state the geometric reason. Do not rely on the diagram looking accurate.
Part A • 10 marks
Short-response questions
Identify the angle relationship when two angles lie on the same side of a transversal and inside two parallel lines. (2 marks)
State the rule for corresponding angles when parallel lines are cut by a transversal. (2 marks)
State the relationship between alternate interior angles. (2 marks)
A corresponding angle is 68°. Find the matching corresponding angle and give a reason. (2 marks)
What total do co-interior angles make when the lines are parallel? (2 marks)
Part B • 25 marks
Extended-response questions
A transversal cuts two parallel lines. One alternate interior angle is 52°. Find a corresponding angle, a co-interior angle and a vertically opposite angle. Show each reason. (5 marks)
Explain how dynamic geometry software can be used to verify corresponding, alternate and co-interior angle relationships. Describe what should remain true as the transversal is dragged. (5 marks)
A scissor-lift mechanism contains repeated crossing bars and parallel supports. Explain how geometric angle relationships help the mechanism move in a controlled and symmetrical way. (5 marks)
A triangle has interior angles 40° and 65°. Find the third interior angle and the exterior angle at that vertex. Explain why the exterior angle also equals the sum of the two opposite interior angles. (5 marks)
Describe how to construct two parallel lines and a transversal using a ruler and set square. Explain how corresponding or alternate angles can be used to check the construction. (5 marks)
Part C • Enrichment
Multi-rule reasoning
11. A transversal intersects two parallel lines. One acute angle is x° and its co-interior partner is 3x°. Find x and all acute/obtuse angle values in the diagram. Justify each step using angle rules.
Part D • Triangle and diagram reasoning
Extra challenge questions
A triangle has an exterior angle of 120°. One opposite interior angle is 50°. Find the other opposite interior angle and give the theorem used.
Triangle ABC has angles 3x°, 4x° and 5x°. Find x and all three angles.
Triangle ABC has angles 50°, x° and (x + 20)°. Find x and all three angles.
A triangle angle is alternate interior to a 48° angle between parallel lines. Find the triangle angle and explain why.
A triangle lies between two parallel lines. A co-interior angle paired with one triangle angle is 140°. Find the triangle angle and state the rule.
Teacher / checking section
Answers
1–5 Short response
1. Co-interior. 2. Corresponding angles are equal. 3. Alternate interior angles are equal. 4. 68°, corresponding angles are equal. 5. 180°.
6. 52° angle chain
Corresponding = 52°. Vertically opposite = 52°. Co-interior = 180° − 52° = 128°.
7. Dynamic geometry
Construct parallel lines and a transversal, measure the relevant pairs, then drag the transversal. Corresponding and alternate pairs remain equal; co-interior pairs continue to sum to 180°.
8. Scissor lift
Credit explanations that connect repeated parallel/crossing members to equal or supplementary angle constraints and controlled, symmetrical linkage motion.
9. Triangle exterior angle
Third interior angle = 180° − 40° − 65° = 75°. Exterior angle = 180° − 75° = 105°, which also equals 40° + 65°.
10. Construction
Hold a set square against a ruler, draw one line, slide the set square without rotating it and draw the second line. Add a transversal. Equal corresponding or alternate angles provide a check of parallelism.
11. Enrichment
x + 3x = 180°, so x = 45°. All acute angles are 45° and all obtuse angles are 135°, using co-interior, corresponding, alternate and vertically opposite angle rules.
12–16 Triangle challenges
12. 70°. 13. x = 15°, angles 45°, 60°, 75°. 14. x = 55°, angles 50°, 55°, 75°. 15. 48°, alternate interior angles are equal. 16. 40°, co-interior angles sum to 180°.