Question

question 25 of 25
is △efg ≅ △hjk? if so, name the postulate that applies.
given:
ef ≅ hj
eg ≅ hk
fg ≅ jk
a. congruent – sss
b. congruent – sas
c. congruent – asa
d. might not be congruent

Explanation:

Step1: Recall Congruence Postulates

SSS (Side - Side - Side) postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. SAS (Side - Angle - Side) requires two sides and the included angle to be congruent, and ASA (Angle - Side - Angle) requires two angles and the included side to be congruent.

Step2: Analyze Given Information

We are given that \(EF\cong HJ\), \(EG\cong HK\), and \(FG\cong JK\). So, all three corresponding sides of \(\triangle EFG\) and \(\triangle HJK\) are congruent.

Step3: Apply the Postulate

Since three sides of \(\triangle EFG\) are congruent to three sides of \(\triangle HJK\), we can apply the SSS congruence postulate. So the triangles are congruent by SSS.

Answer:

A. Congruent - SSS