Question

consider the two triangles shown below.

two right triangles are shown. the first has legs 6 and 8, hypotenuse 10. the second has leg 4.5, leg 6, hypotenuse 7.5. note: the triangles are not drawn to scale.

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: Check side ratios

First, find the ratios of corresponding sides. For the first triangle sides: 6, 8, 10. Second triangle: 4.5, 6, 7.5.
Calculate ratios: $\frac{6}{4.5}=\frac{4}{3}$, $\frac{8}{6}=\frac{4}{3}$, $\frac{10}{7.5}=\frac{4}{3}$. So sides are proportional (scale factor $\frac{4}{3}$), but congruent triangles need equal sides (scale factor 1).

Step2: Compare side lengths

First triangle sides: 6, 8, 10. Second: 4.5, 6, 7.5. No sides are equal (6 vs 4.5, 8 vs 6, 10 vs 7.5). Congruent triangles require all corresponding sides equal (SSS congruence), but here sides are proportional (similar) not equal.

Answer:

B. No