Reasons, not looks
A bridge crosses two parallel river banks. It makes 72° with the near bank. What is the angle in the same corner at the far bank?
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The rule
The angle is 72°. The two angles correspond, and the banks are parallel.
Two facts work in opposite ways.
- Parallel lines given. Find equal angles, or angles that total 180°.
- Equal angles given. Use them to show that lines are parallel.
Both can show 72°. The reason is not the same.
| Given | Wanted | Use |
|---|---|---|
| The banks are parallel. | The angle in the same corner at the far bank. | Corresponding angles are equal. |
| The angles are measured equal. | Are the lines parallel? | Equal angles make lines parallel. |
The bridge. The banks are parallel. The bridge makes 72° with the near bank. The angle in the same corner at the far bank is 72°. The two angles correspond, and corresponding angles are equal.
The gate. A rail cuts two bars. Alternate angles measure 65° and 65°. The bars are parallel, because equal alternate angles make lines parallel.