Question

note: the triangles are not drawn to scale.
are the two triangles congruent?
choose 1 answer:
a yes
b no
c there is not enough information to say.

Explanation:

Step1: Calculate the third angle of the first triangle

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle of the first triangle be \(x\). Then \(x + 37^{\circ}+110^{\circ}=180^{\circ}\), so \(x=180^{\circ}-(37^{\circ} + 110^{\circ})=33^{\circ}\).

Step2: Calculate the third angle of the second triangle

Let the third angle of the second triangle be \(y\). Then \(y+43^{\circ}+100^{\circ}=180^{\circ}\), so \(y = 180^{\circ}-(43^{\circ}+100^{\circ})=37^{\circ}\).

Step3: Check for congruence

Since the angles of the two triangles are not the same (first triangle has angles \(33^{\circ},37^{\circ},110^{\circ}\) and the second has \(37^{\circ},43^{\circ},100^{\circ}\)), and congruent triangles must have all corresponding angles and sides equal. Even though one side is equal (\(5 = 5\)), the angle - side - angle (or other congruence criteria) is not met.

Answer:

B. No