Question

1. determine whether the two triangles are congruent. if they are, state by what theorem they are congruent. the triangles are not to scale.

a. congruent by sas
b. congruent by asa
c. congruent by sss
d. not congruent

1. determine whether the two triangles are congruent. if they are, state by what theorem they are congruent. the triangles are not to scale.

a. congruent by sas
b. congruent by asa
c. congruent by sss
d. not congruent

Explanation:

Step1: Recall congruence theorems

SAS (Side - Angle - Side) requires two sides and the included angle to be equal. ASA (Angle - Side - Angle) requires two angles and the included side to be equal. SSS (Side - Side - Side) requires all three sides to be equal.

Step2: Analyze the first pair of triangles

For the first pair of triangles, we have two angles \(35^{\circ}\) and \(105^{\circ}\) and the side between them (10 m) equal in both triangles. By the ASA (Angle - Side - Angle) congruence theorem, the two triangles are congruent.

Step3: Analyze the second pair of triangles

For the second pair of triangles, we have two sides \(15m\) and \(10m\) and the included angle \(35^{\circ}\) equal in both triangles. By the SAS (Side - Angle - Side) congruence theorem, the two triangles are congruent.

Answer:

1. a. congruent by ASA
2. a. congruent by SAS