Question

Triangles GHI and JKL are similar triangles, and the ratio of the length of GH to the length of JKL is 2:1. Which of the following ratios is also equal to 2:1?

a) HI : KL
b) GI : JL
c) JI : GK
d) HJ : LK

Answer 1

In similar triangles, all corresponding side lengths maintain the same ratio. Therefore, the ratios HI:KL and GI:JL will also be 2:1, reflecting the similarity of triangles GHI and JKL.

Step-by-step explanation:

When triangles are similar, all corresponding side lengths are in proportion, and corresponding angles are equal. If triangles GHI and JKL are similar with a side length ratio of GH:JK = 2:1, then all other corresponding side lengths between the two triangles must also have a 2:1 ratio.

In similar triangles, the ratio of any corresponding side lengths will be the same. That means, option a), HI:KL, and option b), GI:JL, must have the same ratio as GH:JK, which is 2:1. However, option c), JI:GK, and option d), HJ:LK, are not sets of corresponding sides in the similar triangles, so their ratios would not necessarily be 2:1.

Therefore, both a) HI:KL and b) GI:JL will have a 2:1 ratio, the same as the given corresponding sides GH:JK due to the nature of similar triangles.