Exercise 17 Page 379

Looking at the labels on the given figure, we can see that TP = PR = 4, which means TP ≅ PR.

We will start by finding m∠ PRT. We will consider the Isosceles Triangle Theorem.

Using this theorem, let's show the congruent angles and label them as x^(∘).

Now, we can find m ∠ PRT using the Triangle Angle-Sum Theorem.

We found that x=60, so the measures of ∠ PRT and m ∠ PTR are 60^(∘). With this information, we can conclude that △ PTR is an equiangular triangle. Remember that in an equiangular triangle, all sides are congruent. TP ≅ PR ≅ TR Therefore, the value of TR is 4.