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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

6. Similarity Transformations

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Exercise 38 Page 599

To find the missing length, use the Pythagorean Theorem.

13

Practice makes perfect

We want to find the length of BC. Notice that we have two pairs of consecutive congruent sides, BA ≅ AD and BC ≅ CD.

If a quadrilateral is a kite, then its diagonals are perpendicular. Therefore, we know that the given segments are the hypotenuses of two congruent right triangles, and we can use the Pythagorean Theorem to write the following equation. 12^2+ 5^2= CD^2 Let's solve this equation using inverse operations.

12^2+5^2=CD^2

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Solve for CD

Calculate power

144+25=CD^2

Add terms

169=CD^2

Rearrange equation

CD^2=169

sqrt(LHS)=sqrt(RHS)

CD=± 13

CD > 0

CD=13

Since CD ≅ BC, it must be that BC=13.

Subchapter links

Exercises p.596-599