Chapter 8.2, Problem 63SPR

To determine

To explain:

Given triangles are similar or not, if not give reason.

Answer to Problem 63SPR

  $△\mathrm{M}\mathrm{L}\mathrm{J}\sim △\mathrm{P}\mathrm{K}\mathrm{J}$ by AAA similarity.

Explanation of Solution

Given information:

  

Lets assume $△\mathrm{M}\mathrm{L}\mathrm{J}$ and $△\mathrm{P}\mathrm{K}\mathrm{J}$ are two given triangles.

In order to find two triangles to be similar all corresponding sides must be proportional. $\angle \mathrm{J}\cong \angle \mathrm{J}$ due to the reflexive property. Additionally it is prove that $\angle \mathrm{J}\mathrm{P}\mathrm{K}\cong \angle \mathrm{J}\mathrm{M}\mathrm{L}$ because they are corresponding angles formed by parallel lines.

Therefore, $△\mathrm{M}\mathrm{L}\mathrm{J}\sim △\mathrm{P}\mathrm{K}\mathrm{J}$ by AAA similarity.