Question

question 3 of 10
the triangles shown below must be congruent.

two triangles with angles 60°, 61° and side 12, and angles 60°, 61° and side 12

a. true
b. false

Explanation:

Step1: Recall Triangle Congruence

To determine if two triangles are congruent, we can use angle - side - angle (ASA) congruence criterion. The ASA criterion states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.

Step2: Analyze the Given Triangles

In the first triangle, we have angles \(60^{\circ}\) and \(61^{\circ}\), and the included side between these two angles is \(12\). In the second triangle, we also have angles \(60^{\circ}\) and \(61^{\circ}\), and the included side between these two angles is \(12\).

Let's calculate the third angle of each triangle. The sum of the interior angles of a triangle is \(180^{\circ}\). For the first triangle, the third angle \(A_1=180-(60 + 61)=180 - 121 = 59^{\circ}\). For the second triangle, the third angle \(A_2=180-(60 + 61)=180 - 121=59^{\circ}\).

We can see that two angles (\(60^{\circ}\) and \(61^{\circ}\)) and the included side (length \(12\)) of the first triangle are equal to two angles (\(60^{\circ}\) and \(61^{\circ}\)) and the included side (length \(12\)) of the second triangle. By the ASA congruence criterion, the two triangles are congruent.

Answer:

A. True