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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 29 Page 380

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

m∠ CAD=44

Practice makes perfect

Looking at the given figure, we can figure out that AD≅ DC.

Thus, △ ADC 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, ∠ CAD ≅ ∠ ACD which means that m∠ CAD = m∠ ACD. Using this equality, let's find m∠ CAD by the Interior Angles Theorem.

m∠ CAD+m∠ ADC+m∠ ACD=180

m∠ ACD= m∠ CAD, m∠ ADC= 92

m∠ CAD+ 92+ m∠ CAD=180

Add terms

2m∠ CAD+92=180

LHS-92=RHS-92

2m∠ CAD=88

.LHS /2.=.RHS /2.

m∠ CAD=44

Subchapter links

Exercises p.378-382