Evaluate: Whether the provided data is sufficient to demonstrate&nbsp;△WXZ=∼△YZX&nbsp;using the SAS Congruency Theorem. If so, provide evidence; if not, explain why.&nbsp;

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High School
Geometry
High school geometry
Congruence

Braxton Pugh

Answered question

2021-07-22

Evaluate: Whether the provided data is sufficient to demonstrate $△ W X Z \tilde{=} △ Y Z X$ using the SAS Congruency Theorem. If so, provide evidence; if not, explain why.

Answer & Explanation

okomgcae

Skilled2021-07-23Added 93 answers

Calculation:
Recollect the HL Congruence Theorem:
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of second right triangle, then the two triangles are congruent.
From the given figure, the triangles

△ W X Z and △ Y Z X

are two right triangles with

\overset{―}{W X} \tilde{=} \overset{―}{Y Z}

.
By Reflexive Property of Congruence theorem,

\overset{―}{X Z} \tilde{=} \overset{―}{Z X}

.
Therefore, the

△ W X Z and △ Y Z X

are congruent.

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