Foundations for Geometry Review Sheet
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1 Name: Date: Block: Foundations for Geometry Review Sheet Show all work to receive full credit. This is will be collected the day of the test. 1) Draw and define line segment AB: 2) Draw and define ray EF: 3) Draw and define a line containing points X and Y: 4) Draw and define: ABC Use the diagram for questions 5-9 5) Name the Plane: 6) Name a segment: 7) Name a ray: 8) Name 3 collinear points: P N E A L 9) Name 3 non-collinear points: 10) H is between I and J. (Hint: Draw a picture) a. HI = 7.9 and HJ = Find IJ. b. JI = 56 and IH = 23. Find HJ. c. H is the midpoint of IJ, and IH = Find HJ. d. H is the midpoint of IJ, and IJ = Find IH. 1
2 11) Find the length of LM. K L M x x - 2 3x ) A pole-vaulter uses a 18-foot-long pole. She grips the pole so that the segment below her left hand is twice the length of the segment above her left hand. Her right hand grips the pole 2.5 feet above her left hand. How far up the pole is her right hand? 13) Name 8 different angles in the figure: A C D B 14) T is in the interior of PQR. Find each of the following. a. m PQT if m PQR = 42º and m RQT = 12º P T R b. m PQR if m PQR = (10x - 7)º, m RQT = 5xº and m PQT = (4x + 6)º Q c. m PQR if QT bisects PQR, m RQT = (10x - 13)º and m PQT = (6x + 1)º 2
3 15) PQR and SQR form a linear pair. Find the sum of their measures. 16) Name the ray that PQR and SQR share. 17) Supplement of Z 42.1º 18) Complement of Y Z 19) An angle s measure is 12 degrees less than three times its supplement. Find the measure of the angle. 20) An angle is its own complement. Find the measure of a supplement to its angle. 21) DEF and FEG are complementary. m DEF = (3x - 4)º, and m FEG = (5x + 6)º. Find the measure of both angles. 3
4 22) DEF and FEG are supplementary. m DEF = (9x + 1)º and m FEG = (8x + 9)º. Find the measures of both angles. 23) Name all the possible pairs of vertical angles ) Name all the possible linear pairs of angles. 25) Use your compass and straightedge to construct angle bisector DG to CDE 26) Use your compass and straightedge to construct a congruent angle DEF to ABC 4
5 27) Use your compass and straightedge to construct a segment congruent to XY X Y 28) Use your compass and straightedge to construct a segment bisector through AB. A B 29) Draw and label an acute, obtuse and right angle. 5
6 30) A rectangular box of tissues is 9.5 inches long, 4.5 inches wide and 4 inches high. Find the area of the surface of the box. 31) What is the perimeter of a rectangle whose width is (x 7) units and whose length is (3x + 10) units? 32) Find the area and circumference of the circle. 33) Find the perimeter and area. 34) Find the perimeter and area. 6
7 35) Find the perimeter and area. 36) Find the circumference and area of the circle. Use the π key on your calculator. Round to the nearest tenth. 37) Find the circumference and area of the circle. Use the π key on your calculator. Round to the nearest tenth. 38) Find the circumference and area of the circle. Use the π key on your calculator. Round to the nearest tenth. 7
8 39) In a rowing race, the distance between the teams in first and second place is 5.7 meters. The distance between the teams in second and third place is one-third that distance. How much farther ahead is the team in first place than the team in third? 40) On a subway route, station C is located at the midpoint between stations A and D. Station B is located at the midpoint between stations A and C. If the distance between stations A and D is 2.4 kilometers, what is the distance between stations B and D? 41) Use the figure to name each of the following. three collinear points four coplanar points a plane containing E 42) During a football game, a quarterback standing at the 8-yard line passes the ball to a receiver at the 26-yard line. The receiver then runs with the ball halfway to the 50-yard line. How many total yards (passing plus running) did the team gain on the play? 8
9 43) R and S are complementary. If m R = (7 + 3x) and m S = (2x + 13), Find the measure of each angle. 44) The base of a triangular garden measures 5.5 feet. Its height is 3 feet. If 4 pounds of mulch are needed to cover a square foot, how many pounds of mulch will be needed to cover the garden? 45) The measure of an angle is (12x 15). What is the measure of its complement? What is the measure of its supplement? 46) What is the difference between a linear pair and two angles which are supplementary? 9
10 47) A rectangular counter 3 feet wide and 5 feet long has a circle cut out of it in order to have a sink installed. The circle has a diameter of 18 inches. What is the approximate area of the remaining countertop surface? If you have any questions, please see me prior to the day of your test. smilardo.wordpress.com - homework: worksheets: link to book and 10
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