AZMERIT GEOMETRY REVIEW

Transcription

1 ZMERIT GEOMETRY REVIEW NME: HPTER 2 Rewrite the conditional statement in if-then form. Then write the converse, inverse, and contrapositive of the conditional statement. Decide whether each statement is true or false. 1. It is noon when the clock strikes n angle measure of 87 is an acute angle. HPTER 3 3. Identify all pairs of angles of the given type.. lternate interior. lternate exterior. orresponding D. onsecutive interior 4. Find the value of x and state which theorem you used.

2 5. Find the value of x and state which theorem you used. 6. Find m 1, m 2, and m 3. Explain your reasoning Given: 1 2 and 2 3 Prove: 1 4 STTEMENTS RESONS c d a b

3 HPTER 4 8. Justify the last two steps of the proof. Given: and Prove: R S T U Proof: Given Given Symmetric Property of ; SSS. Reflexive Property of ; SSS. Reflexive Property of ; SS D. Symmetric Property of ; SS 9. Name the angle included by the sides and N M P... D. none of these

4 )( 10. State whether and are congruent. Justify your answer yes, by either SSS or SS. yes, by SSS only. yes, by SS only D. No; there is not enough information to conclude that the triangles are congruent. 11. Is there enough information to prove the two triangles congruent? If yes, write the congruence statement and name the postulate you would use. If no, write not possible and tell what other information you would need. Q S P R 12. Which two triangles are congruent by S? N M O P Q R... D. None

5 13. From the information in the diagram, can you prove? Explain.. yes, by S. yes, by SS. yes, by D. no 14. What is the value of x? E D x º 93.5 F Drawing not to scale D Is there enough information to conclude that the two triangles are congruent? If so, what is a correct congruence statement? D. Yes;.. Yes;.. Yes;. D. No, the triangles cannot be proven congruent.

6 HPTER 5 Solve for X One of the acute angles in a right triangle has a measure of 35. What is the measure of the other acute angle? 20. E D GIVEN: DE, & Point is the midpoint of E PROVE: ED

7 HPTER company builds trusses to support structures. In the truss shown below, the support is the midsegment of. Find the value of x. H x ft G 21 ft a ft c. 21 ft b. 63 ft d. 42 ft 22. You install fencing around your large triangular garden. Then, you divide it into four small triangular gardens by connecting the midpoints of each side of the triangle with fencing. How many feet of fencing do you need? K H 21 ft 17 ft G 19 ft a. 228 ft c. 171 ft b. 177 ft d. 114 ft 23. Find D a. = 15 c. = 24 b. = 30 d. = 9

8 24. Find. 4x + 6 5x - 6 D a. = 20 c. = 54 b. = 10 d. = In the diagram, bisects Find D. 6x + 3 D 3x + 6 a. D = 12 c. D = 9 b. D = 1 d. D = List the sides of from shortest to longest a.,, c.,, b.,, d.,,

9 HPTER 7 Find the sum of the measures of the interior angles of the indicated convex Polygon. 27. octagon gon The sum of the measures of the interior angles of a convex polygon is given. lassify the polygon by the number of sides Find the value of each variable in the parallelogram Show that the quadrilateral with vertices at Q 0, 3, R 0, 6, S 6, 0, and T 3, 0 is a trapezoid. Decide whether the trapezoid is isosceles. Then find the length of the midsegment of the trapezoid. Find m K and m L. 34.

10 HPTER 8 The figures are similar. Find the missing corresponding side length. 35. Figure has a perimeter of 60 inches and one of the side lengths is 5 inches. Figure has a perimeter of 84 inches. 36. Figure has an area of 4928 square feet and one of the side lengths is 88 feet. Figure has an area of 77 square feet. Show that the two triangles are similar. 37. EG and EDF 38. WZY and YXW 39. Use the figure to find the values of x, y, and z that makes DEF ~ GHF.

11 40. Given: LN 2x MN 2y NP x NQ y Prove: MLN ~ PQN STTEMENTS 1. LN 2 MN 2 NP x NQ y RESONS LN NP MN NQ 2x x 2y y LN MN 3. NP NQ 4. LNM QNP MLN ~ PQN 5. HPTER 9 Solve the triangle. Round decimal answers to the nearest tenth

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13 Find the area of the triangles HPTER 10 Solve for the variable(s)

14 Write the standard equation of a circle that is tangent to the y-axis, with the center located at 4, 6. Then Graph the ircle. HPTER The circumference of a circle is 34 centimeters. Find the radius of this circle. a. about cm c. about 5.41 cm b. about cm d. about cm 55. The diameter of is 14 centimeters. Find the arc length of. R P 34 Q 14 cm S a. about cm c. about 4.15 cm b. about cm d. about 8.31 cm

15 56. Find the area of the rhombus. 2 m 5 m 5 m 2 m a. 10 c. 20 b. 29 d Identify and describe the solid produced by rotating the figure around the given axis a. cylinder with radius 5 c. cone with radius 5 b. cone with radius 10 d. cylinder with radius 5

16 58. Find the volume of the prism. 5 cm 13 cm 13 cm 59. Find the volume of the cylinder. 5.5 cm 7.8 cm a. about c. about b. about d. about Find the volume of the composite solid. 9 in. 12 in. 12 in. 12 in. a c b d. 1728

17 61. Find the volume of the cone. 7 m 2 m a. about c. about 7.33 b. about d. about snowball has a radius of 7 centimeters. What is the volume? 7 cm a. about c. about b. about d. about 196

18 HPTER 12 Find the number of possible outcomes in the sample space. Then list the possible outcomes. 63. stack of cards contains the thirteen clubs from a standard deck of cards. You pick a card from the stack and flip two coins. 64. You spin a spinner with the numbers 1 5 on it and roll a die. Determine whether the events are independent. Explain your reasoning. 65. You have three white golf balls and two yellow golf balls in a bag. You randomly select one golf ball to hit now and another golf ball to place in your pocket. Use a sample space to determine whether randomly selecting a white golf ball first and then a white golf ball second are independent events.