Question

Which of the following theorems verifies that XYZ - UWV

A. HL
B. AA
C. LL
D. HA

Answer 1

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.