Question

1. which congruence rule can be used to show that the two triangles are congruent?

a. ssa
b. sas
c. asa
d. not enough information

1. which is the correct congruency statement for the following triangles?

a. \\( \triangle s q p \cong \triangle r t q \\)
b. \\( \triangle s q p \cong \triangle t r q \\)
c. \\( \triangle p q s \cong \triangle t q r \\)
d. \\( \triangle p q s \cong \triangle t r q \\)

Explanation:

Question 34

Step1: Recall congruence rules

SSA (Side - Side - Angle) is not a valid congruence rule. ASA (Angle - Side - Angle) requires two angles and the included side. SAS (Side - Angle - Side) requires two sides and the included angle.

Step2: Analyze the given triangles

From the figure, we have two sides (marked with equal signs) and one non - included angle. But if we consider the common side (the side where the two triangles meet), we actually have two sides and the included angle.

Step1: Identify corresponding parts

In \(\triangle SQP\) and \(\triangle RTQ\):

• \(SP = RT\) (marked with equal signs)
• \(SQ=RQ\) (from the figure)
• \(\angle SQP=\angle RQT\) (vertically opposite angles)

Step2: Write the congruence statement

By SAS (Side - Angle - Side) congruence rule, \(\triangle SQP\cong\triangle RTQ\)

Answer:

B. SAS

Question 35