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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 32 Page 380

Consider the Isosceles Triangle Theorem and use the Interior Angles Theorem.

m∠ ABC=22^(∘)

Practice makes perfect

In the previous exercise, we found that m∠ ACB=136^(∘). We can also see that AC≅ BC by the markings.

Thus, △ ACB is isosceles. In this case, we should consider the Isosceles Triangle Theorem.

If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Using the theorem, let's show the congruent angles.

As we can see, ∠ CAB ≅ ∠ ABC which means that m∠ CAB = m∠ ABC. Using this equality, let's find m∠ ABC by the Interior Angles Theorem.

m∠ CAB + m∠ ABC+m∠ ACB=180

m∠ CAB= m∠ ABC, m∠ ACB= 136

m∠ ABC+m∠ ABC+ 136=180

Add terms

2m∠ ABC+136=180

LHS-136=RHS-136

2m∠ ABC=44

.LHS /2.=.RHS /2.

m∠ ABC=22

Thus, m∠ ABC is 22^(∘).

Subchapter links

Exercises p.378-382