: Select the best answer from the choices provided. (Each question is worth one point) 1. By what corollary is this true: AD/AB=AB/AC Leg-Hypotenuse geometric mean corollary Altitude-hypotenuse geometric mean corollary neither 2. If DC=12 cm and AD=3 cm, then BD=___. 4 cm 15 cm 6 cm 3. AD/AB=AB/AC. If AD=9 cm and DC=4 cm, then AB= ___ and BC= ___. 3 cm and 3âˆš13 cm 3âˆš13 cm and 2âˆš13 cm 5 cm and 13 cm 4. Î”ABC is a right triangle and DB is the altitude to hypotenuse AC. If DB=10 cm and CD=20 cm, find AB. 50 cm 5âˆš5 40 cm 5. If x is the geometric mean between q and r, solve x in terms of q and r. x=qr x=(qr)2 x=âˆš(qr) 6. Consider the right triangle above. Side a has length âˆš13 cm and side b has length 6 cm. Find the length of side c. âˆš26 cm âˆš19 cm 7 cm 7. Consider the following right triangle. Side a has length 5 cm and side c has length 2âˆš10 cm. Find the length of side b. âˆš50 cm âˆš15 cm âˆš65 cm 8. An isosceles triangle has a base of 8 m. The length of the altitude to the base is 3 m. Find the lengths of the congruent sides. 3 m 2âˆš3 m 5 m 9. The length of one side of an equilateral triangle is 10 cm. Find the altitude of the triangle. 5 cm 5âˆš5 cm 5âˆš3 cm 10. Find the length of the altitude of an equilateral triangle if one side has a length of 6 cm. 3âˆš5 cm 3âˆš3 cm 6âˆš2 cm 11. The hypotenuse of an isosceles right triangle is 8 inches. Find the length of the legs. 4âˆš2 in 8 in 2âˆš2 in 12. Find the altitude of an equilateral triangle if one of its sides measures 12 cm. 3âˆš6 cm 6âˆš3 cm 6âˆš5 cm 13. The measurements of a rectangular box are: l=12 cm, w=4 cm, h=3 cm Find the length of the diagonal GC shown in the figure. 14 cm 15 cm 13 cm 14. Find the measure of the diagonal of one face of a cube whose side measures 12 cm. 12 cm 12âˆš3 cm 12âˆš2 cm 15. The roof of a schoolhouse is shaped like an isosceles triangle. The base of the triangle measures 8 meters and one side measures 5 meters. Find the altitude. 4 meters 3 meters 7 meters 16. A tent is pitched such that it creates an equilateral triangle. If each of the congruent sides measure 2 meters, what is the height of the tent? 2 m âˆš2 m âˆš3 m 17. An equilateral triangle has an altitude of 7 cm. Find the length of one side. 7âˆš2 cm (14âˆš3)/3 cm 7âˆš3 cm 18. In an isosceles right triangle, one of the congruent sides has a measure 7 cm. Find the measure of the hypotenuse. 4âˆš3 cm 7 7âˆš2 cm 7âˆš3 cm 4 19. The hypotenuse of an isosceles right triangle is 2 cm. Find the measure of one of its legs. âˆš2 cm 2 cm âˆš2/2 cm 20. If b=6âˆš3 cm, then a=___ and c=___. 9 cm and 6âˆš6 cm 9 cm and 12âˆš3 cm 6 cm and 12 cm 21. If c=10 cm, then a=___ and b=___. 5âˆš3 cm and 10âˆš3 cm 5 cm and 5âˆš3 cm 10âˆš3 cm and 20 cm 22. If c=12âˆš3 cm, then a=___ and b=___. 6âˆš3 cm and 18 cm 6âˆš3 cm and 24 cm 24 cm and 24âˆš3 cm 23. A square has a diagonal of length 10 cm. What is the perimeter of the square? 10âˆš2 cm 20âˆš2 cm 5âˆš2 cm 24. What is the square of âˆš10? 2âˆš10 10 5 25. What is the square of 3âˆšb? 3b 6b 9b 26. What is the perimeter of a square with a diagonal of 3âˆš2? 3 12 18 27. What is the length of a diagonal of a square with a side of length 8? 8 8âˆš2 2 28. What is the length of the diagonal of a square with a 15-decimeter side? 15âˆš2 dm 15 dm âˆš2 dm 29. What is the length of one side of a square with a 16-centimeter diagonal? âˆš12 cm 8âˆš2 cm âˆš16 cm 30. The perimeter of a square is 48 m. What is the length of a side and a diagonal? 10 m; 144 m 8 m; 12 m 12 m; 12âˆš2 m Part 2 Short Answer: Type your response in the text box below each item. If necessary, spell out mathematical symbols. (Each question is worth five points) 31. In trapezoid NDKF, NL and DG are altitudes, mâˆ F=45Âº, mâˆ K=30Âº, DG=8, and ND=10. Find DK, GK, FN, mâˆ GDK, mâˆ FNL, and the perimeter. 32. Given: ABCD is a trapezoid. Î”AYD is congruent to Î”BCY. ABYD is a rhombus. AD=3 and AX=1. Find the length of all sides and diagonals.