Question

1. which pair of triangles can be proven congruent using the sas congruence postulate?

Explanation:

Step1: Recall SAS Congruence

SAS (Side - Angle - Side) congruence postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Analyze each pair

• First pair (left - most triangles): Check the marked sides and angles. The markings do not clearly show two sides and the included angle congruence.
• Second pair (triangle \(ABC\) and \(XYZ\)): The markings on the sides and angles: In \(\triangle ABC\) and \(\triangle XYZ\), we can see that two sides and the included angle are marked as congruent (the tick marks on the sides and the angle marks). So, by SAS, \(\triangle ABC\cong\triangle XYZ\).
• Third pair (triangle \(GKH\) and \(JKH\)): The right angle and the common side \(KH\), but the other side and angle markings do not fit SAS as well as the second pair.

Answer:

The pair of triangles \( \triangle ABC \) and \( \triangle XYZ \) (the middle - pair of triangles) can be proven congruent using the SAS Congruence Postulate.