---
title: "Parallel lines: cheat sheet"
subtitle: "Angles and shapes"
---

# Parallel lines

> The words and methods from this unit, with an example of each.

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**transversal**: Parallel lines go the same way and never meet; arrows (>>) mark them. A transversal crosses both, making eight angles.

$$\text{parallel lines} \gg \text{ crossed by a transversal}$$

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**corresponding angles**: The same place at each crossing (an F shape). With parallel lines they are equal.

$$a = e$$

_a and e: the same place at each crossing, both 120°_

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**alternate angles**: Between the parallel lines, on opposite sides of the transversal (a Z shape). With parallel lines they are equal.

$$c = f$$

_c and f: between the lines, opposite sides, both 60°_

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**co-interior angles**: Between the parallel lines, on the same side (a C shape). With parallel lines they add to $180^\circ$: they are not equal unless both are $90^\circ$.

$$c + e = 180^\circ$$

_c and e: between the lines, same side, 60° + 120° = 180°_

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**vertically opposite angles**: Opposite each other at one crossing: always equal, parallel lines or not. Not one of the parallel-line pairs.

$$b = c$$

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**give a reason**: For each angle you find, name the rule: corresponding or alternate angles are equal; co-interior angles add to $180^\circ$; angles on a straight line add to $180^\circ$.

$$f = 70^\circ \;\text{(corresponding to } b\text{)}$$

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