1 Answer

MyItchyChin · Answer 1 · 2022-02-18T16:49:37+0000

Given:

The figure of two triangle XYZ and UWV.

To find:

The theorem that is used to verify
$\Delta XYZ\sim \Delta UWV$ .

Solution:

In triangle XYZ,

$m\angle X+m\angle Y+m\angle Z=180^\circ$ (Angle sum property)

$70^\circ+90^\circ+m\angle Z=180^\circ$

$160^\circ+m\angle Z=180^\circ$

$m\angle Z=180^\circ-160^\circ$

$m\angle Z=20^\circ$

In triangle XYZ and triangle UWV,

$m\angle Y\cong m\angle W$ (Right angles)

$m\angle Z\cong m\angle V$ (Equal measures)

Two angles of one triangle are congruent to corresponding angles of another triangle. So, the triangles are similar by AA property of similarity.

$\Delta XYZ\sim \Delta UWV$ (AA similarity theorem)

Therefore, the correct option is B.

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