Question

note: the triangles are not drawn to scale. are the two triangles congruent?

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 \(x + 66^{\circ}+49^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-(66^{\circ}+49^{\circ})=65^{\circ}\).

Step2: Calculate the third angle of the second triangle

Let the third angle of the second triangle be \(y\). Then \(y + 74^{\circ}+63^{\circ}=180^{\circ}\), so \(y = 180^{\circ}-(74^{\circ}+63^{\circ}) = 43^{\circ}\).

Step3: Check congruence

For two triangles to be congruent (by ASA, AAS, SSS, SAS criteria), their corresponding angles and sides must be equal. The first triangle has angles \(49^{\circ},66^{\circ},65^{\circ}\) and a side of length \(7\). The second triangle has angles \(43^{\circ},63^{\circ},74^{\circ}\) and a side of length \(7\). Since the angles are not the same (corresponding angles are not equal), the two triangles are not congruent.

Answer:

No, the two triangles are not congruent.