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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

5. Solving Quadratic Equations by Using the Quadratic Formula

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Exercise 60 Page 139

How many different isosceles triangles can you create? Find the value of x for each of them.

See solution.

Practice makes perfect

We are given an isosceles triangle. However, we do not know which two sides are congruent. Thus, we have three cases.

Case 1

If the sides shown in the figure are congruent, then x=64^(∘) by definition.

Case 2

If the sides shown in the figure are congruent, then the other angle is equal to x^(∘).

By the Triangle Angle Sum Theorem, x^(∘)=58 ^(∘). x^(∘)+ x^(∘)+64^(∘)=180^(∘) ⇔ x^(∘)=58^(∘)

Case 3

If the sides shown in the figure are congruent, then the other angle is equal to 64^(∘).

By the Triangle Angle Sum Theorem, x^(∘)=52 ^(∘). x^(∘)+ 64^(∘)+64^(∘)=180^(∘) ⇔ x^(∘)=52^(∘) As a result, the value of x is 64, 58, or 52.

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Exercises p.137-139