SECTION A.2 Geometry Essentials A19 Because the triangles are similar, corresponding angles are equal. So A 90 , = ° B 60 , = ° and C 30 . = ° Also, the corresponding sides are proportional. That is, x 3 5 6 . = We solve this equation for x . Solution x x x x x x 3 5 6 5 3 5 5 6 3 30 10 = ⋅ = ⋅ = = Multiply both sides by x5 . Simplify. Divide both sides by 3. The missing length is 10 units. Now Work problem 43 Skill Building In Problems 13–18, the lengths of the legs of a right triangle are given. Find the hypotenuse. 13. a b 5, 12 = = 14. a b 6, 8 = = 15. a b 10, 24 = = 16. a b 4, 3 = = 17. a b 7, 24 = = 18. a b 14, 48 = = In Problems 19–26, the lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 19. 3, 4, 5 20. 6, 8, 10 21. 4, 5, 6 22. 2, 2, 3 23. 7, 24, 25 24. 10, 24, 26 25. 6, 4, 3 26. 5, 4, 7 Concepts and Vocabulary A.2 Assess Your Understanding 1. A(n) triangle is one that contains an angle of 90 degrees. The longest side is called the . 2. For a triangle with base b and altitude h , a formula for the area A is . 3. The formula for the circumference C of a circle of radius r is . 4. Two triangles are if corresponding angles are equal and the lengths of the corresponding sides are proportional. 5. Multiple Choice Which of the following is not a case for determining congruent triangles? (a) Angle–Side–Angle (b) Side–Angle–Side (c) Angle–Angle–Angle (d) Side–Side–Side 6. Multiple Choice Choose the formula for the volume of a sphere of radius r . (a) r 4 3 2 π (b) r 4 3 3 π (c) r 4 3 π (d) r 4 2 π 7. True or False In a right triangle, the square of the length of the longest side equals the sum of the squares of the lengths of the other two sides. 8. True or False The triangle with sides of lengths 6, 8, and 10 is a right triangle. 9. True or False The surface area of a sphere of radius r is r 4 3 .2 π 10. True or False The triangles shown are congruent. 29 29 30 30 10 10 11. True or False The triangles shown are similar. 1005 1005 255 255 12. True or False The triangles shown are similar. 1205 1205 2 3 4 3 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure
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