AMSCO'S Geometry. New York - Rye High School

514 Ratio, Proportion, and SimilarityExercisesWriting About Mathematics1. When altitude CD is drawn to the hypotenuse of right triangle ABC, it is possible thatACD and BCD are congruent as well as similar. Explain when ACD BCD.2. The altitude to the hypotenuse of right RST separates the hypotenuse, RS, into two congruentsegments. What must be true about RST?Developing SkillsIn 3–12, ABC is a right triangle with ACB the right angle. Altitude CD intersects AB at D. Ineach case find the required length.3. If AD 3 and CD 6, find DB. 4. If AB 8 and AC 4, find AD.5. If AC 10 and AD 5, find AB. 6. If AC 6 and AB 9, find AD.7. If AD 4 and DB 9, find CD. 8. If DB 4 and BC 10, find AB.9. If AD 3 and DB 27, find CD. 10. If AD 2 and AB 18, find AC.11. If DB 8 and AB 18, find BC. 12. If AD 3 and DB 9, find AC.Applying SkillsIn 13–21, the altitude to the hypotenuse of a right triangle divides the hypotenuse into two segments.13. If the lengths of the segments are 5 inches and 20 inches, find the length of the altitude.14. If the length of the altitude is 8 feet and the length of the shorter segment is 2 feet, find thelength of the longer segment.15. If the ratio of the lengths of the segments is 1: 9 and the length of the altitude is 6 meters,find the lengths of the two segments.16. The altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into twosegments of lengths 4 and 5. What is the length of the altitude?17. If the length of the altitude to the hypotenuse of a right triangle is 8, and the length of thehypotenuse is 20, what are the lengths of the segments of the hypotenuse? (Let x and20 x be the lengths of the segments of the hypotenuse.)18. The altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into segmentsof lengths 2 and 16. What are the lengths of the legs of the triangle?19. In a right triangle whose hypotenuse measures 50 centimeters, the shorter leg measures 30centimeters. Find the measure of the projection of the shorter leg on the hypotenuse.20. The segments formed by the altitude to the hypotenuse of right triangle ABC measure 8inches and 10 inches. Find the length of the shorter leg of ABC.21. The measures of the segments formed by the altitude to the hypotenuse of a right triangleare in the ratio 1 : 4. The length of the altitude is 14.a. Find the measure of each segment.b. Express, in simplest radical form, the length of each leg.