Question

consider the two triangles shown below.

two triangles are shown, not drawn to scale. first triangle: sides 5, 7, and an angle of 38° between sides 5 and 7. second triangle: sides 6, 8, and an angle of 54° between sides 6 and? (the third side is marked?)

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: Recall congruence criteria

Congruent triangles must have all corresponding sides and angles equal. We check side - angle relationships. For the first triangle, sides are 5, 7 and an included angle of \(38^{\circ}\). For the second triangle, sides are 6, 8 and an included angle of \(54^{\circ}\). The side - length ratios: \(\frac{5}{6}
eq\frac{7}{8}\) (since \(\frac{5}{6}\approx0.83\) and \(\frac{7}{8} = 0.875\)), and the included angles are different (\(38^{\circ}
eq54^{\circ}\)). So the triangles do not satisfy SAS (Side - Angle - Side) congruence, and other congruence criteria (SSS, ASA, AAS) also don't hold as the sides and angles don't match.

Step2: Conclude

Since the corresponding sides and angles are not equal, the triangles are not congruent.

Answer:

B. No