ALLEN PARK HIGH SCHOOL i r s t S e m e s t e r R e v i e w G EOMERY APHS/MAH Winter 2010
DIRECIONS his section of test is 68 items, which you will work in this booklet. Mark the correct answer as directed by your teacher. You may use a calculator that has been approved by your teacher. Only your test booklet and calculator may be used; no other materials should be on your desk. 1 he statement, 4 is an even number, and all even numbers are divisible by 2; therefore, 4 is divisible by 2, is a form of reasoning. or questions 2-4, use the following statement. If there is a lot of snow on the ground, it must be cold. 2 State the Converse on the conditional statement. 3 State the Inverse of the conditional statement. 4 State the Contrapositive of the conditional statement. 5 he table below shows the truth values for statements p and q. Complete the third column for the truth value of the statement p or not q, symbolized p ~ q. Circle the correct answer. p q p ~ q A. B. C. D. APHS/MAH 1 GO ON O HE NEX PAGE
6 he table below shows the truth values for statements p and q. Complete the third column for the truth value of the statement q and not p, symbolized q p. p q q p 7 Given the statement, If it is icy outside, then the roads are slippery. ind a statement which would be considered logically equivalent. Use the figure below to answer questions 9 15 given that lines n, m, and l are parallel. 8 ind all of the remaining angles. 9 What is the relationship for 15 and 19? n 1 2 10 What is the relationship for 2 and 10? 11 What is the relationship for 18 and 20? 12 What is the relationship for 12 and 14? m l 3 4 5 6 105 7 8 9 10 11 12 13 65 14 15 16 17 18 19 20 21 22 23 13 What is the relationship for 7 and 8? 14 What is the relationship for 5 and 6? p 24 25 26 q 15 If m 22 (7x 15) and m 17 25, find x. 16 Define the following: Point Line Plane Angle Ray Postulate heorem Corollary - APHS/MAH 2 GO ON O HE NEX PAGE
17 he proof of a geometric situation is shown below. ill in the remaining. D W X G Y Given: D WX, G XY Prove: DG WY Statement Reasons 1. D WX, G XY 1. Given 2. D WX, G XY 2. Definition of 3. DG, WY 3. Segment Addition Postulate 4. DG 4. Substitution Property 5. DG WY 5.? 6. DG WY 6. Definition of congruent segments 18 he diagram below shows two mitre cuts of baseboards for a floor. he measures of the angles formed are shown in the diagram, in terms of x and y. ind the value of x and y. 2y + 5 9y - 45 7x + 20 3x 19 In the figure below, XYZ measures 80, YZX measures 55, and points W, X, and Y are collinear. What is the measure of WXZ? Y X W Z APHS/MAH 3 GO ON O HE NEX PAGE
6 ft Use the figure to answer questions 20 24. 3 ft 20 What is the perimeter of the rectangle represented by the drawing above? 21 What is the area of the rectangle represented by the drawing above? 22 What is the area of the triangle represented by the drawing above? 23 What is the relationship between the area of the rectangle and area of the triangle? 24 What is the length of the diagonal in the rectangle represented by the drawing above? 25 In the figure below, XYZ measures 80, YZX measures 55, and points W, X, and Y are collinear. What is the measure of WXZ? Y X W Z APHS/MAH 4 GO ON O HE NEX PAGE
60 70 110 80 100 90 100 80 70 110 120 50 120 60 130 U S 40 130 50 140 140 40 30 150 30 150 V 20 160 20 160 10 170 10 170 R X W 26 Using the protractor above, find the measure of RXU. 27 Using the protractor above, find the measure of WX. 28 Using the protractor above, find the measure of RXS. 29 Using the protractor above, find the measure of XV. 30 Using the protractor above, find the measure of UXV. xy coordinate plane, a line segment has its endpoints at 7,12 and 13,4. What are the coordinates of the midpoint of the line segment? 31 In the standard, 32 In the standard, at xy coordinate plane, a line segment has an endpoint at 2,5 and a midpoint 7,10. What are the coordinates of the other endpoint of the line segment? APHS/MAH 5 GO ON O HE NEX PAGE
33 In the standard xy, coordinate plane, a line segment has an endpoint at 3,5 and another endpoint at 5,4. Determine the length of the segment? 34 While constructing a center drain for a circular pool, the length of pipe needed to be dug out is 13 feet. Using 3.14 for, what is the approximate area, in square feet, of the bottom of the pool? 35 he proof of a geometric situation is shown below. K J L Given: JLM is isosceles. MK bisects JL. Prove: J L M Statement Reasons 1. JLM is isosceles, MK bisects JL 1. Given 2. JM LM 2. Definition of 3. JK LK 3. Definition of 4.? 4. Reflexive 5. JKM LKM 5.? 6.? 6.? 36 If one leg of a right triangle is 10 inches long, and the hypotenuse is 14 inches long, how many inches long is the triangle s other leg? 37 he three angles of a triangle are 2 x, 5x 20, and x 48. ind x and the largest angle. APHS/MAH 6 GO ON O HE NEX PAGE
38 A builder has a wooden board measuring 224 inches long. He needs to cut this board to make 12 plaques. What should the length of each plaque be? 39 he coordinates xy, on the Cartesian coordinate plane of the vertices of a triangle are X 2,3, Y 2,6, and Z 7,3. Calculate the perimeter of XYZ. 40 In the figure below, what is the value of the missing angles? 55 5 20 1 2 3 4 41 Calculate the perimeter RS if it is an equilateral triangle with RS = 4x - 8, S 2x 10, and R = 5x - 17. 42 In the figure MQ NQ, MNP = 110 and NQP 80. ind all remaining angles. M Q N P APHS/MAH 7 GO ON O HE NEX PAGE
Use the figure to answer. D A B 43 Determine which postulate, if any, can be used to prove that ABD CBD when AD CD and DB is an angle bisector. C 44 Determine which postulate, if any, can be used to prove that ABD CBD when BAD BCD and B is the midpoint of AC. 45 Determine which postulate, if any, can be used to prove that ABD CBD when AB CB and DB AC. 46 Use the Pythagorean theorem to find the distance of the hypotenuse of the triangle below. A. 4 3 4 B. 2 26 2 C. 2 13 5 D. 52 APHS/MAH 8 GO ON O HE NEX PAGE
47 he diagram below demonstrates the construction of copying an angle. S and V are radii of circle XW and XY are radii of circle X S W V X Y Which triangle congruence pattern can be used to justify that SV WXY? Use the figure to answer. A 2 C 5 B -2 48 In the triangle graphed above, what is the slope of line segment AB? 49 In the triangle graphed above, what is the slope of line segment BC? 50 Using the answers from the previous two questions to classify ABC. APHS/MAH 9 GO ON O HE NEX PAGE
51 ind m KGH if GK bisects GH, m GK 7w 3and GH 104. x y G K H 52 ind the length of each side of the triangle below if the perimeter is 49 units. 2 n + 2 2 n 3 53 ind the surface area and volume of the solid. 4 5 10 54 ind the volume of the solid. 3 4 5 6 55 What is the relationship between plane B and MN? APHS/MAH 10 GO ON O HE NEX PAGE
56 he measures of two complementary angles are 6y 3and 4y 13. ind the measure of each angle. 57 ind the area of the figure. 16 yd 10 yd 20 yd 58 ind the area of the figure. 14 m 19 m 19 m 14 m 59 ind the area of the figure. 24 24 32 60 ind the slope of MN. y M (0, 4) Q ( 3, 0) O N (3, 0) x P (0, 3) APHS/MAH 11 GO ON O HE NEX PAGE
61 Identify the congruence transformation as a flip, turn, or slide. y ' H G H' G' x 62 ind the volume of the figure. 12.8 in. 14 in. 63 ind the volume of the figure. 20 m 24 m 64 ind the volume of the figure. 30 m 17 m 65 ind the lateral area of the figure. 37 m 24 m APHS/MAH 12 GO ON O HE NEX PAGE
66 ind the area of the figure. 8 4 5 67 What are the missing coordinates of the triangle? 68 Position and label the triangle on the coordinate plane. Isosceles LMN with base LN 2b units long a. y b. M ( b, c) y L(0, 2 b) N ( c, b) O L (0, 0) N (2 b, 0) x O M(0, 0) x c. y d. L ( b, c) y N (0, 2 b) L ( c, b) O M(0, 0) N (2 b, 0) x O M(0, 0) x APHS/MAH 13 GO ON O HE NEX PAGE
If you finish early, you may go back and check your work. SOP APHS/MAH SOP DO NO GO ON