Question

3. Using Postulates and/or Theorems learned in Unit 1, determine whether PRQ ~ MRN. Show all your work and explain why the triangles are similar or why they are not..
https://drive.google.com/open?id=17uaEBY6haJkj7_H3C5lYLKOyXvGj9K7f

Answer 1

The triangles PRQ and MRN has a congruent angle, the angle in vertex R is a common angle, a right angle (angle of 90°):
1) Angle PRQ of triangle PRQ is congruent with angle MRN of triangle MRN

The sides that form the congruent angle in triangle PRQ has a proportion of:
(Major side) / (Minor side) = RQ / PR = 18 / 12 = 1.500

The sides that form the congruent angle in triangle MRN has a proportion of:
(Major side) / (Minor side) = MR / RN = 8 / 6 = 1.333

2) The side that form the congruent angle are not proportionals (1.500 in triangle PRQ and 1.333 in triangle MRN).

Conclusion: The triangles are not similars.

Answer: The triangles are not similars