Question

Which of the following conditions are sufficient to show that triangle ABC sim triangle QPR

Select all that apply.

A. m angle Q = 63

B. m angle R = 81

D. m angle P = 81

C. RP = 4.5

Answer 1

C. RP = 4.5

Explanation:

You want to know what condition is sufficient to show ∆ABC ~ ∆QPR, given three sides and 2 angles in ∆ABC, and 2 sides in ∆QPR.

Similarity

Similarity can be shown if all three sides are proportional, or if two angles are congruent.

The offered answer choices only list one angle, so none of those will work. The answer choice that makes the third side of ∆QPR be in the same proportion as the corresponding side of ∆ABC is the condition of interest.

C. RP = 4.5

__

Additional comment

The side ratios in the two triangles are ...

AB : BC : CA = 10 : 9 : 6

QP : PR : RQ = 5 : PR : 3

For these ratios to be the same, PR must be half of BC, just as the other segments in ∆QPR are half their counterparts in ∆ABC.