Given: YZ || UV Prove: XY/XU = YZ/UV
Answers: XY/XU = YZ/UV, If lines ||, alternate internal angles (<'s) =, Vertical angles (<'s) =, YZ || UV, Definition of Similar Polygons, angle(YZV) = angle(UVZ), Given, XYZ ~ XUV, YXZ = VXU, AA

Answer and Step-by-step explanation:

We just need to put these steps in order.

First, use the fact that YZ || UV. If these lines are parallel, then we have alternate internal angles that are equal. <YZV and <UVZ are alternate interior angles, so they are equal.

Now, look at the two "middle" angles: <YXZ and <VXU. These are called vertical angles and they are formed at the intersection of two lines; by definition, they're always equal. So, that means <YXZ = <VXU.

Now, we have two pairs of equal angles, so we can use the AA similarity theorem to prove that ΔYXZ ~ ΔUXV. By definition of similar polygons, corresponding sides have the same ratio. XY corresponds to XU and YZ corresponds to UV, so we have the equivalence: XY/XU = YZ/UV.

Thus, the steps are:

1. If lines YZ and UV are ||, alternate internal angles (<'s): angle(YZV) = angle(UVZ)

2. Vertical angles (<'s): YXZ = VXU

3. AA

4. XYZ ~ XUV

5. Definition of Similar Polygons: XY/XU = YZ/UV

Hope this helps!

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