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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

5. Isosceles and Equilateral Triangles

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Exercise 17 Page 379

Use the Isosceles Triangle Theorem.

TR=4

Practice makes perfect

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.

Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

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.

m ∠ PRT+m ∠ PTR+m ∠ TPR=180

SubstituteValues

Substitute values

x+x+60=180

Add terms

2x+60=180

LHS-60=RHS-60

2x=120

.LHS /2.=.RHS /2.

x=60

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.

Subchapter links

Exercises p.378-382