Name Date Chapter 6 Review In Exercises 1 4, find the indicated measure. State how you know. 1. AD 2. GJ 3. PQ 4. m DGF 5.In the figure at the right, what value of x makes G the incenter of JKL? 6. LG 6x 14, NG 3x 22 Find MG and NG. 195
In Exercises 7 9, point Q is the centroid of indicated segment lengths. JKL. Use the given information to find the 7. AQ 21 8. JA 72 9. KQ 10 Find QL and AL. Find JQ and QA. Find QA and KA. 10.When LV 9, what is UW? LU 2 x 5 and VW 8 x, what is LM? 11.When 12.When 2 LV? NL 2x 12 x and UW x 4, what is 13.When UV 2y 14 and MN 13 y, what is WN? In Exercises 14 and 15, list the angles of the given triangle from smallest to largest. 14. 15. In Exercises 16 and 17, list the sides of the given triangle from shortest to longest. 16. 17. 196
In Exercises 18 and 19, is it possible to construct a triangle with the given side lengths? Explain. 18. 15, 37, 53 19. 9, 16, 8 20. List the angles of the given triangle from smallest to largest. In Exercises 21 24, copy and complete the statement with,, or. Explain your reasoning. 21. AC DF 22. m HGI m IGJ 23. m 1 m 2 24. KL MN In Exercises 25 and 26, write and solve an inequality for the possible values of x. 25. 26. 197
Chapter 7 Review 1. Find the sum of the measures of the interior angles of a heptagon (7-sides). 2. The sum of the measures of the interior angles of a convex polygon is 3060. Classify the polygon by the number of sides. 3. Find the measure of each interior and exterior angle of a regular 30-gon. In Exercises 4 8, find the value of each variable in the parallelogram. 4. 5. 6. 7. In Exercises 8-11, state how you know the quadrilateral is a parallelogram. 8. 9. 10. 11. 198
Three vertices of parallelogram ABCD are given. Find the remaining vertex. 12. A 2, 0, B 2, 2, D 2, 2 13. A 1, 3, C 1, 2, D 1, 2 Decide whether quadrilateral JKLM is a rectangle, a rhombus, or a square. Give all names that apply. Explain your reasoning. 14. J 3, 5, K 7, 6, L 6, 2, M 2, 1 15. J 4, 1, K 1, 5, L 5, 2, M 2, 4 The diagonals of rhombus ABCD intersect at M. Given that m MAB 53, MB 16, and AM 12, find the indicated measure. 16. m AMD 17. m ADM 18. m ACD 19. DM 20. AC Find the value of x. 21. 22. 199
Find the length of the midsegment of the trapezoid with the given vertices. 23. A 0, 3, B 4, 5, C 4, 2, D 0, 2 24. E 3, 3, F 1, 3, G 3, 3, H 5, 3 Give the most specific name for the quadrilateral. Explain your reasoning. 25. 26. Find m K and m L. 27. 28. 200
Final Review- Chapter 8 In Exercises 1 and 2, find the scale factor. Then list all pairs of congruent angles and write the ratios of the corresponding side lengths in a statement of proportionality. 1. LMN QRS 2. ABCD EFGH In Exercises 3 and 4, the polygons are similar. Find the value of x. 3. 4. In Exercises 5 11, ABC XYZ. 5.Find the scale factor of ABC to XYZ. 6.Find m X. 7. Find CD. 8.Find the area of ABC. Then find the area of XYZ. 9.Find the ratio of the area of ABC to the area of XYZ. 10.Find BC and YZ. Explain your reasoning. 11.Find the ratio of the perimeter of ABC to the perimeter of XYZ. 201
In Exercises 12 and 13, determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning. 12. 13. In Exercises 3 and 4, show that the two triangles are similar. 14. ABD and ACE 15. WXZ and ZXY 16.In the diagram, ABC EDC. a.is AB DE? b.find m CAD. c. Find ED. In Exercises 2 and 3, find the value of x that makes PQR JKL. 17. 18. 19.Verify that TUV XYZ. Find the scale factor of TUV to XYZ. TUV: TU 15, UV 21, TV 18 XYZ: XY 35, YZ 49, XZ 42 202
In Exercises 20, find the length of AB. 20. In Exercises 21 and 22, determine whether QR ST. 21. 22. In Exercises 23, find the length of the indicated line segment. 23. DF In Exercise 24, find the value of the variable. 24. Chapter 9 Final Review In Exercises 1 6, find the value of x. Then tell whether the side lengths form a Pythagorean triple. 1. 2. 3. 203
In Exercises 4 and 5, tell whether the triangle is a right triangle. 4. 5. In Exercises 6 and 7, verify that the segment lengths form a triangle. Is the triangle acute, right, or obtuse? 6. 5, 12, and 13 7. 5, 7, and 8 In Exercises 1 3, find the value of x. Write your answer in simplest form. 8. 9. 10. In Exercises 11 13, find the values of x and y. Write your answers in simplest form. 11. 12. 13. In Exercises 14 and 15, identify the similar triangles. 14. 15. 204
In Exercises 16 and 15, find the value of x. 16. 17. In Exercises 18 and 19, find the geometric mean of the two numbers. 18. 3 and 12 19. 4 and 14 In Exercises 20 22, find the value of x. Round your answer to the nearest tenth. 20. 21. 22. Find the tangents of the acute angles in the right triangle. Write each answer as a fraction and as a decimal rounded to four decimal places. In Exercises 23 and 24, find sin J, sin K, cos J, and cos K. Write each answer as a fraction and as a decimal rounded to four places. 23. 24. 205
In Exercises 25 and 26, find the value of each variable using sine and cosine. Round your answers to the nearest tent 25. In Exercises 1 3, determine which of the two acute angles has the given trigonometric ratio. 27.The sine of the angle is 8 17. 28.The cosine of the angle is 15 17. 29.The tangent of the angle is 15 8. In Exercises 4 6, let B be an acute angle. Use a calculator to approximate the measure of B to the nearest tenth of a degree. 30. sin B 0.64 31. cos B 0.12 32. tan B 2.18 Chapter 11 Review In Exercises 1 4, find the indicated measure. 1. radius of a circle with a circumference of 42 meters 2. circumference of a circle with a radius of 27 feet 3. circumference of a circle with a diameter of 15 inches 4. diameter of a circle with circumference 39 centimeters 206
In Exercises 6 8, find the arc length of AB. 5. 6. 7. In Exercises 9 and 10, find the perimeter of the region. 8. 9. In Exercises 7 10, find the areas of the sectors formed by 10. 11. JLK. 12.Find the area of H. 13. Find the area of M. 207
In Exercises 13 15, find the area of the shaded region. 15. 15. In Exercises 1 4, find the area of the kite or rhombus. 16. 17. In Exercises 13 17, find the area of the regular polygon. 18. 19. In Exercises 20 21, tell whether the solid is a polyhedron. If it is, name the polyhedron. 20. 21. 208
22.Is the block shown a polyhedron? Explain your reasoning. In Exercises 23 and 24, find the volume of the prism. 23. 24. In Exercises 24 and 25, find the volume of the cylinder. 24. 25. In Exercises 26 and 27, find the missing dimension. 3 3 26. Volume 240 m 27. Volume 1244 in. 209