Question

name the postulate or theorem that can be used to show that the triangles are congruent. then explain why the statement below is true.
et≅mt
name the postulate or theorem that can be used to show that the triangles are congruent. choose the correct answer below.
a angle - side - angle (asa) postulate
b side - side - side (sss) postulate
c side - angle - side (sas) postulate
d angle - angle - side (aas) theorem

Explanation:

• In the given figure, we have two triangles \( \triangle AET\) and \( \triangle AMT\).
• We know that \( \angle EAT=\angle MAT\) (given as marked angles at \(A\)), \(AT = AT\) (common side), and \( \angle ATE=\angle ATM\) (given as marked angles at \(T\)).
• The Angle - Side - Angle (ASA) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. Here, in \( \triangle AET\) and \( \triangle AMT\), \( \angle EAT\cong\angle MAT\), \(AT\cong AT\), and \( \angle ATE\cong\angle ATM\). So, by ASA postulate \( \triangle AET\cong\triangle AMT\).
• Since \( \triangle AET\cong\triangle AMT\), their corresponding parts are congruent. So, \(ET\cong MT\) (corresponding parts of congruent triangles are congruent - CPCTC).

Answer:

A. angle - side - angle (ASA) postulate. The statement \(ET\cong MT\) is true because \( \triangle AET\cong\triangle AMT\) (by ASA postulate) and corresponding parts of congruent triangles are congruent (CPCTC).