Question

consider the two triangles shown below.

two right triangles are shown, the first with legs 6 and 8, hypotenuse 10; the second with leg 4.5, base 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 are 6, 8, 10. For the second, 4.5, 6, 7.5.
Calculate ratios: $\frac{4.5}{6} = 0.75$, $\frac{6}{8} = 0.75$, $\frac{7.5}{10} = 0.75$.

Step2: Determine congruence

Congruent triangles have equal corresponding sides (SSS congruence). But here, sides are in proportion (scaled by 0.75), meaning they are similar, not congruent (since sides aren't equal, just proportional).

Answer:

B. No