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Year 7 · Geometric Reasoning

Parallel
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Year 7 · Geometric Reasoning

Parallel Lines & a Transversal

When a single straight line — the transversal — crosses two or more parallel lines, the same angle pattern repeats at every intersection. Master the four relationships below and you can find every unknown angle in the figure from a single given.

Worked Example

Three parallel lines, one transversal, one given angle of 110°. Find a, b, c, d.

The four named relationships:
① Angles on a straight line — sum to 180° (linear pair).
② Vertically opposite — equal (the X-cross).
③ Corresponding angles — equal (same quadrant at a different intersection — F-shape).
④ Alternate angles — equal (Z-shape between the parallel lines, OR outside them).
⑤ Co-interior — sum to 180° (between parallel lines, same side of transversal — C-shape).

A two-step chain

You almost never need more than two relationships in a row. The shortest path from given → unknown is usually:

  1. Find an angle at the same intersection as your unknown (linear pair, vertically opposite, corresponding, alternate, or co-interior with the given).
  2. If it's already the unknown — done. Otherwise apply one more local rule (linear pair or vertically opposite) at that intersection.

What's coming

Fifteen diagrams, graded by how much guidance you get:

Type the value as a number — degrees are implied. Whole numbers only (no decimals); the answer is always between 1° and 179°.

Parallel Lines  ·  Find every unknown
Complete

All Fifteen Solved

📐

You've worked through every diagram. Find-the-unknown problems on parallel lines come down to recognising the right relationship — and that's the skill the test rewards.

The five rules you've practised:
① Angles on a straight line — sum to 180°
② Vertically opposite — equal (the X-cross)
③ Corresponding — equal (same quadrant at a different intersection — F-shape)
④ Alternate — equal (Z-shape between parallel lines, or outside them)
⑤ Co-interior — sum to 180° (between parallel lines, same side of the transversal — C-shape)