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

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JannetPalos JannetPalos · Answer 1 · 2019-01-20T16:54:39+01:00

Answer:

∠ Y = ∠ V

∠ Z = ∠ W

[tex]\frac{XY}{XV} =\frac{YZ}{VW} =\frac{XZ}{XW}[/tex]

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,

[tex]\frac{XY}{XV} =\frac{YZ}{VW} =\frac{XZ}{XW}[/tex]

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ChiKesselman ChiKesselman · Answer 2 · 2019-10-17T08:05:59+02:00

Answer:

[tex]\triangle XYZ \sim \triangle XVW[/tex]

Step-by-step explanation:

We are given the following information in the question:

[tex]\triangle XYZ \sim \triangle XVW[/tex]

The, the above triangles enjoy the following properties:

1. Congruent angles

Corresponding angles of similar triangle are equal.

[tex]\angle{XYZ} = \angle{XVW}\\\angle{YZX} = \angle{VWX}\\\angle{ZXY} = \angle{WXV}[/tex]

2 Corresponding sides are in proportion.

[tex]\displaystyle\frac{XY}{XV} = \frac{YZ}{VW} =\frac{XZ}{XW}[/tex]

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