Question

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

Answer 1

`\triangle XYZ \sim \triangle XVW`

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(XY)/(XV) = (YZ)/(VW) =(XZ)/(XW)`

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

Answer 2

∠ Y = ∠ V

∠ Z = ∠ W

`(XY)/(XV) =(YZ)/(VW) =(XZ)/(XW)`

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,

`(XY)/(XV) =(YZ)/(VW) =(XZ)/(XW)`