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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 26 Page 396

Consider the Triangle Angle-Sum Theorem and Isosceles Triangle Theorem.

v=76

Practice makes perfect

Before we begin, let's add some labels to the given diagram.

As we can see, AC and BC are congruent. Therefore, let's recall the Isosceles Triangle Theorem.

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

By this theorem, we can conclude that ∠ A and ∠ B are congruent. With this information, we measure of ∠ A is also 52^(∘).

Now, to find the value of v, we can use the Triangle Angle-Sum Theorem. m∠ A+ m∠ B+ m∠ C=180 ⇓ 52+52+v=180 Let's solve this equation for v.

52+52+v=180

Add terms

104+v=180

LHS-104=RHS-104

v=76

Subchapter links

1 Angles of Triangles p.394

2 Congruent Triangles p.394

3 Proving Triangles Congruent-SSS, SAS p.395

4 Proving Triangles Congruent-ASA, AAS p.395

5 Isosceles and Equilateral Triangles p.396

6 Triangles and Coordinate Proof p.396