Length and Measurement Examples

If m∠XYZ = 37°, what is the measure of ∠1?

Since ∠XYZ and ∠1 are vertical angles, ∠1 is also 37°.

What is the measurement of ∠UWV? 

The only clue we're given is that it's marked with a box. That little box tells us that ∠UWV is a right angle, measuring 90°.

What word best describes the relationship between lines WV and YU?

They cross each other, so they can't be parallel. We could say that they're intersecting lines, but there's an even better word to describe them. Since they meet at a 90° angle (thanks, ∠UWV), they are perpendicular lines.

Suppose that ZY ≅ YX, YX ≅ XW, and XW ≅ WV. If WV is 5 inches in length, what is the measurement of ZY?

Since WV measures 5 inches and is congruent to XW, we know XW also measures 5 inches. But then that means YX also measures 5 inches (since YX ≅ XW) and finally, ZY measures 5 inches (ZY ≅ YX). For brownie points, which property did we use to solve this problem? If you thought transitive, you thought right.