Question

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Complete the proof. Below is a drag and drop geometric proof. Complete the proof in your notebook. Choose from these possible answers: Given YZ UV

Answer 1

YZ || UV - Given

YXZ = VXU - Vertical triangles =

YZV = UVZ - If lines ||, alternate internal triangles =

XYZ ~ XUV - AA

XY/XU = YZ/UV - Definition of Similar Polygons

Answer 2

Explanation:

∠YXZ and ∠VXU are vertical angles, and therefore are congruent.

∠YXZ ≅ ∠VXU, Vertical ∠'s ≅

Next, we're given that lines YZ and UV are parallel. That means that ∠YZV and ∠UVZ are alternate interior angles, and therefore congruent.

∠YZV ≅ ∠UVZ, If lines ||, then alternate interior ∠'s ≅

If two triangles have two pairs of congruent angles, then the third pair must also be congruent, making the two triangles similar.

△XYZ ~ △XUV, AA

Since the triangles are similar, then by definition, their sides are proportional.

XY/XU = YZ/UV, Definition of Similar Polygons