Question

note: the triangles are not drawn to scale.
are the two triangles congruent?
choose 1 answer:
a yes
b no

Explanation:

Step1: Calculate the third angle of the first triangle

The sum of angles in a triangle is \(180^{\circ}\). For the first triangle with angles \(72^{\circ}\) and \(63^{\circ}\), the third angle is \(180-(72 + 63)=45^{\circ}\).

Step2: Check congruence using ASA (Angle - Side - Angle) criterion

Both triangles have angles \(45^{\circ}\), \(63^{\circ}\) and a side of length \(3\) between these angles. By the ASA congruence criterion, 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.

Answer:

A. Yes