Mai has proven that triangle WYZ is congruent to triangle WYX using the Side-Side-Side Triangle Congruence Theorem. Why can she now conclude that diagonal WY bisects angles ZWX and ZYX?

A) Because WZ is congruent to WX
B) Because YZ is congruent to YX
C) Because triangle WYZ is isosceles
D) Because the triangles share side WY

Question

22-12-2023
Mathematics

High School

Thank you for visiting Mai has proven that triangle WYZ is congruent to triangle WYX using the Side Side Side Triangle Congruence Theorem Why can she now conclude that. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

Mai has proven that triangle WYZ is congruent to triangle WYX using the Side-Side-Side Triangle Congruence Theorem. Why can she now conclude that diagonal WY bisects angles ZWX and ZYX?

A) Because WZ is congruent to WX
B) Because YZ is congruent to YX
C) Because triangle WYZ is isosceles
D) Because the triangles share side WY

Answer :

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Stella506 Stella506 · Answer 1 · 2024-10-19T04:41:48-04:00

Final answer:

The diagonal WY bisects angles ZWX and ZYX because triangle WYZ is congruent to triangle WYX via the side-side-side congruence theorem, meaning corresponding angles of these congruent triangles are equal.

Explanation:

Mai can conclude that diagonal WY bisects angles ZWX and ZYX because triangle WYZ is congruent to triangle WYX by the Side-Side-Side (SSS) congruence theorem. This theorem states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent. As a consequence of this congruence, corresponding angles of congruent triangles are also congruent.

In this case, angle ZYW (formed by sides ZY and WY) corresponds to angle XYW (formed by sides XY and WY) in the congruent triangle, and angle ZWY (formed by sides WZ and YZ) corresponds to angle XWY (formed by sides WX and YX) in the congruent triangle. Therefore, these two pairs of angles must be equal.

Learn more about Triangle Congruency here:

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