Question

the triangles shown below must be congruent.
a. true
b. false

Explanation:

Step1: Analyze triangle angles

In a triangle, the sum of angles is \(180^\circ\). For each triangle, calculate the third angle: \(180 - 80 - 51 = 49^\circ\). Both triangles have angles \(51^\circ\), \(80^\circ\), \(49^\circ\), and a side of length 10 between the \(51^\circ\) and \(80^\circ\) angles (ASA congruence criterion: Angle - Side - Angle).

Step2: Apply ASA congruence

ASA (Angle - Side - Angle) states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent. Here, the included side (length 10) between \(51^\circ\) and \(80^\circ\) angles is equal, and the angles are equal. So the triangles must be congruent.

Answer:

A. True