Question

Please help me
Show your work
10 points

Answer 1

Triangles PRQ and MRN are not similar.

Explanation:

The two triangles are PRQ and MRN.

It is given that both the triangles have ∠R = 90° as the common angle.

Now, we check whether the ratios of the sides are equal or not.

i.e. To check if
`(PR)/(MR)=(QR)/(NR)`

Since, we have the lengths,

PM = 8, MR = 10. Thus, PR = 8 + 10 = 18

QN = 14, NR = 7. Thus, QR = 14 + 7 = 21

So, we get,

`(PR)/(MR)=(QR)/(NR)`

implies
`(18)/(10)=(21)/(7)`

implies 1.8 = 3, which is not true.

So, the ratio of the sides are not equal.

Hence, we get that the triangle PRQ and MRN are not similar.