Question

Triangle xyz is similar to triangle xvw. write the congruence statements that must be true.

Answer 1

Answer:

∠ Y = ∠ V

∠ Z = ∠ W

$\frac{XY}{XV} =\frac{YZ}{VW} =\frac{XZ}{XW}$

Step-by-step explanation:

It is given that Δ XYZ is similar to Δ XVW.

Since corresponding angles of similar triangles are equal,

∠ X = ∠ X

∠ Y = ∠ V

∠ Z = ∠ W

Also, since corresponding sides of similar triangles are in proportionate,

$\frac{XY}{XV} =\frac{YZ}{VW} =\frac{XZ}{XW}$

Answer 2

Answer:

$\triangle XYZ \sim \triangle XVW$

Step-by-step explanation:

We are given the following information in the question:

$\triangle XYZ \sim \triangle XVW$

The, the above triangles enjoy the following properties:

1. Congruent angles

Corresponding angles of similar triangle are equal.

$\angle{XYZ} = \angle{XVW}\\\angle{YZX} = \angle{VWX}\\\angle{ZXY} = \angle{WXV}$

2 Corresponding sides are in proportion.

$\displaystyle\frac{XY}{XV} = \frac{YZ}{VW} =\frac{XZ}{XW}$

It may be noted that similar triangles are not same as congruent triangles. They are different.