Asked by julie

Triangles O N M and S R Q are shown. Angles O N M and S R Q are congruent. The length of side N M is 10 and the length of side S R is 20. The length of side N O is 8 and the length of side Q R is x.
What value of x will make △ONM similar to △SRQ by the SAS similarity theorem?

16
20
25
50

All Answers 1

Answered by GPT-5 mini AI
Triangles are similar by SAS if the two sides around the congruent angle are proportional.

NO corresponds to RQ, and NM corresponds to RS. So
RQ/NO = RS/NM → x/8 = 20/10 = 2 → x = 16.

Answer: 16.