Chapter 1 Exam. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. 1.

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1 Name: lass: ate: I: hapter 1 Exam Multiple hoice Identify the choice that best completes the statement or answers the question. 1. bisects, m = (7x 1), and m = (4x + 8). Find m. a. m = c. m = 40 b. m = 3 d. m = 0. Find the measure of O. Then, classify the angle as acute, right, or obtuse. a. m O = 15 ; obtuse c. m O = 90 ; right b. m O = 35 ; acute d. m O = 160 ; obtuse 3. billiard ball bounces off the sides of a rectangular billiards table in such a way that 1 3, 4 6, and 3 and 4 are complementary. If m 1 = 6.5, find m 3, m 4, and m Tell whether 1 and 3 are only adjacent, adjacent and form a linear pair, or not adjacent. a. m 3 = 6.5 ; m 4 = 63.5 ; m 5 = 63.5 b. m 3 = 6.5 ; m 4 = 63.5 ; m 5 = 53 c. m 3 = 63.5 ; m 4 = 6.5 ; m 5 = 53 d. m 3 = 6.5 ; m 4 = ; m 5 = 6.5 a. not adjacent b. only adjacent c. adjacent and form a linear pair 1

2 Name: I: 5. Tell whether F and 3 are only adjacent, adjacent and form a linear pair, or not adjacent. 8. Find and EF. Then determine if EF. a. adjacent and form a linear pair b. only adjacent c. not adjacent 6. Use the istance Formula and the Pythagorean Theorem to find the distance, to the nearest tenth, from T(4, ) to U(, 3). a. 1.0 units b. 3.4 units c. 0.0 units d. 7.8 units a. = 13, EF = 13, EF b. = 5, EF = 13, EF c. = 13, EF = 3 5, EF d. = 5, EF = 5, EF 9. Sketch a figure that shows two coplanar lines that do not intersect, but one of the lines is the intersection of two planes. a. 7. There are four fruit trees in the corners of a square backyard with 30-ft sides. What is the distance between the apple tree and the plum tree P to the nearest tenth? b. a. 4.4 ft b. 4.3 ft c ft d ft

3 Name: I: c. 11. The width of a rectangular mirror is 3 4 the measure of the length of the mirror. If the area is 19 in, what are the length and width of the mirror? a. length = 4 in., width = 8 in. b. length = 16 in., width = 1 in. c. length = 48 in., width = 4 in. d. length = 5 in., width = 71 in. 1. Find the coordinates for the image of EFG after the translation (x, y) (x 6, y + ). raw the image. d. 10. Find the circumference and area of the circle. Use 3.14 for π, and round your answer to the nearest tenth. a. a. = 01.0 ft; = 50. ft b. = 50. ft; = 5.1 ft c. = 5.1 ft; = 50. ft d. = 50. ft; = 01.0 ft 3

4 Name: I: b. c. 13. Find the measure of the supplement of R, where m R = (8z + 10) a. (170 8z) b. (190 8z) c d. (80 8z) 14. M is the midpoint of N, has coordinates ( 6, 6), and M has coordinates (1, ). Find the coordinates of N. a. (8, 10) b. ( 5, 4) c. ( 1, ) d. (8 1, 91 ) 15. K is the midpoint of JL. JK = 6x and KL = 3x + 3. Find JK, KL, and JL. a. JK = 1, KL = 1, JL = b. JK = 6, KL = 6, JL = 1 c. JK = 1, KL = 1, JL = 6 d. JK = 18, KL = 18, JL = 36 d. 16. n angle measures degrees more than 3 times its complement. Find the measure of its complement. a. 68 b. 7 c. 3 d. 4

5 Name: I: 17. The map shows a linear section of Highway 35. Today, the Ybarras plan to drive the 360 miles from Springfield to Junction ity. They will stop for lunch in Roseburg, which is at the midpoint of the trip. If they have already traveled 55 miles this morning, how much farther must they travel before they stop for lunch? a. 15 mi c. 180 mi b. 145 mi d. 305 mi 18. Tell whether 1 and are only adjacent, adjacent and form a linear pair, or not adjacent. 0. Find the perimeter and area of the figure. a. perimeter = 6x + 14; area = 3x + 4 b. perimeter = 7x + 14; area = 3x + 4 c. perimeter = 7x + 14; area = 6x + 48 d. perimeter = 7x + 14; area = 6x + 14 a. only adjacent b. adjacent and form a linear pair c. not adjacent 19. is between and E. E = 6x, = 4x + 8, and E = 7. Find E. 1. The rectangles on a quilt are in. wide and 3 in. long. The perimeter of each rectangle is made by a pattern of red thread. If there are 30 rectangles in the quilt, how much red thread will be needed? a. 10 in. b. 150 in. c. 180 in. d. 300 in. a. E = 17.5 b. E = 78 c. E = 105 d. E = 57 5

6 Name: I:. R is the midpoint of. T is the midpoint of. S is the midpoint of. Use the diagram to find the coordinates of T, the area of RST, and. Round your answers to the nearest tenth. 3. The tip of a pendulum at rest sits at point. uring an experiment, a physics student sets the pendulum in motion. The tip of the pendulum swings back and forth along part of a circular path from point to point. uring each swing the tip passes through point. Name all the angles in the diagram. a. T(3, 1); area of RST = 8; 17.9 b. T(3, 1); area of RST = 3; 17.9 c. T(3, 1); area of RST = 16; 8.9 d. T(3, 1); area of RST = 8; 8.9 a. O, O b. O, O, O c. O, O, O, O d. O, O, O Numeric Response 4. Find the measure of the angle formed by the hands of a clock when it is 7: The supplement of an angle is 6 more than five times its complement. Find the measure of the angle. 6

7 I: hapter 1 Exam nswer Section MULTIPLE HOIE 1. NS: Step 1 Solve for x. m = m efinition of angle bisector. (7x 1) = (4x + 8) Substitute 7x 1 for and 4x + 8 for. 7x = 4x + 9 dd 1 to both sides. 3x = 9 Subtract 4x from both sides. x = 3 ivide both sides by 3. Step Find m. m = 7x 1 = 7(3) 1 = 0 heck your simplification technique. Substitute this value of x into the expression for the angle. This answer is the entire angle. ivide by two. orrect! PTS: 1 IF: verage REF: Page 3 OJ: Finding the Measure of an ngle NT: 1..1.f ST: GE1.0 TOP: 1-3 Measuring and onstructing ngles KEY: angle bisectors angle measures. NS: y the Protractor Postulate, m O = m O m O. First, measure O and O. m O = m O m O = = 90 Thus, O is a right angle. To find the measure of angle O, subtract the measure of angle O from the measure of angle O. The sum of the measure of angle O and the measure of angle O is equal to the measure of angle O. orrect! Use the Protractor Postulate. PTS: 1 IF: verage REF: Page 1 OJ: 1-3. Measuring and lassifying ngles NT: 1..1.f ST: GE1.0 TOP: 1-3 Measuring and onstructing ngles KEY: measuring angles classifying angles right acuta obtuse protractor 1

8 I: 3. NS: Since 1 3, m 1 m 3. Thus m 3 = 6.5. Since 3 and 4 are complementary, m 4 = = Since 4 6, m 4 m 6. Thus m 6 = y the ngle ddition Postulate, 180 = m 4 + m 5 + m 6 = m Thus, m 5 = 53. The measure of angle 5 is 180 degrees minus the sum of the measure of angle 4 and the measure of angle 6. orrect! ngle 1 and angle 3 are congruent. ongruent angles have the same measure. ngle 3 and angle 4 are complementary, not supplementary. PTS: 1 IF: verage REF: Page 30 OJ: Problem-Solving pplication NT: g ST: 6MG. TOP: 1-4 Pairs of ngles KEY: application complementary angles supplementary angles 4. NS: 1 and 3 have a common vertex,, but no common side. So 1 and 3 are not adjacent. orrect! Two angles are adjacent if they have a common vertex and a common side, but no common interior points. djacent angles form a linear pair if and only if their noncommon sides are opposite rays. PTS: 1 IF: verage REF: Page 8 OJ: Identifying ngle Pairs NT: g ST: 6MG.1 TOP: 1-4 Pairs of ngles KEY: angle pairs linear pair adjacent

9 I: 5. NS: F and 3 are adjacent angles. Their noncommon sides, F also form a linear pair. and G, are opposite rays, so F and 3 orrect! djacent angles form a linear pair if and only if their noncommon sides are opposite rays. Two angles are adjacent if they have a common vertex and a common side, but no common interior points. PTS: 1 IF: verage REF: Page 8 OJ: Identifying ngle Pairs NT: g ST: 6MG.1 TOP: 1-4 Pairs of ngles KEY: angle pairs linear pair adjacent 3

10 I: 6. NS: Method 1 Substitute the values for the coordinates of T and U into the istance Formula. TU = Ê Ë Áx x 1 ˆ + Ê Ë Á y y 1 ˆ Method Use the Pythagorean Theorem. Plot the points on a coordinate plane. Then draw a right triangle. = ( 4) + ( 3 ) = ( 6) + ( 5) = units ount the units for sides a and b. a = 6 and b = 5. Then apply the Pythagorean Theorem. c = a + b = = = 61 c 7.8 units The distance is the square root of the quantity (x x1)^ + (y y1)^. The distance is the square root of the quantity (x x1)^ + (y y1)^. The distance is the square root of the quantity (x x1)^ + (y y1)^. orrect! PTS: 1 IF: verage REF: Page 45 OJ: Finding istances in the oordinate Plane NT: 1..1.e ST: GE15.0 TOP: 1-6 Midpoint and istance in the oordinate Plane KEY: congruent segments distance formula Pythagorean Theorem 4

11 I: 7. NS: Set up the yard on a coordinate plane so that the apple tree is at the origin, the fig tree F has coordinates (30, 0), the plum tree P has coordinates (30, 30), and the nectarine tree N has coordinates (0, 30). The distance between the apple tree and the plum tree is P. P = Ê Ë Áx x 1 ˆ + Ê Ë Á y y 1 ˆ = ( 30 0) + ( 30 0) = = = ft orrect! heck your calculations and rounding. Set up the yard on a coordinate plane so that the apple tree is at the origin. Then use the distance formula to find the distance. Set up the yard on a coordinate plane so that the apple tree is at the origin. Then use the distance formula to find the distance. PTS: 1 IF: verage REF: Page 46 OJ: pplication NT: 1..1.e ST: GE15.0 TOP: 1-6 Midpoint and istance in the oordinate Plane KEY: application distance formula 5

12 I: 8. NS: Step 1 Find the coordinates of each point. (0, 4), (3, ), E(, 1), and F( 4, ) Step Use the istance Formula. d = (x x 1 ) + (y y 1 ) = ( 3 0) + ( 4) EF = ( 4 ( )) + ( 1) = 3 + ( ) = ( ) + ( 3) = = 13 = = 13 Since = EF, EF. orrect! The square of a negative number is positive. Subtracting a negative number is the same as adding the number. ( ) =. Use the distance formula after finding the coordinates of each point. PTS: 1 IF: verage REF: Page 44 OJ: Using the istance Formula NT: 1..1.e ST: GE17.0 TOP: 1-6 Midpoint and istance in the oordinate Plane KEY: congruent segments distance formula 6

13 I: 9. NS: In the diagram, lines m and l both lie in plane R, but do not intersect. Moreover, line l is the intersection of planes R and W. Is either of the two lines the intersection of the two planes? orrect! The two lines in this diagram intersect. The two lines in this diagram are not coplanar. PTS: 1 IF: verage REF: Page 8 OJ: Representing Intersections NT: b ST: GE1.0 TOP: 1-1 Understanding Points Lines and Planes KEY: points lines planes 10. NS: = πr = π ( 4) 5.1 ft = πr = π ( 4) 50. ft Use the radius, not the diameter, in your calculations. The circumference of a circle is times pi times the radius. The area of a circle is pi times the radius squared. orrect! Use the radius, not the diameter, in your calculations. PTS: 1 IF: verage REF: Page 37 OJ: Finding the ircumference and rea of a ircle NT: 1..1.h ST: GE8.0 TOP: 1-5 Using Formulas in Geometry KEY: circles circumference area 7

14 I: 11. NS: The area of a rectangle is found by multiplying the length and width. Let l represent the length of the mirror. Then the width of the mirror is 3 4 l. = lw 19 = l( 3 4 l) 19 = 3 4 l 56 = l 16 = l The length of the mirror is 16 inches. The width of the mirror is 3 (16) = 1 inches. 4 First, find the length. Then, use substitution to find the width. orrect! First, find the length. Then, use substitution to find the width. The formula for the area of a rectangle is length times width. PTS: 1 IF: dvanced NT: 1..1.h ST: GE8.0 TOP: 1-5 Using Formulas in Geometry KEY: area rectangles application 1. NS: Step 1 Find the coordinates of EFG. The vertices of EFG are E(3, 0), F(1, ), and G(5, 4). Step pply the rule to find the vertices of the image. E'(3 6, 0 + ) = E'( 3, ) F'(1 6, + ) = F'( 5, 0) G'(5 6, 4 + ) = G'( 1, ) Step 3 Plot the points. Then finish drawing the image by using a straightedge to connect the vertices. orrect! To find coordinates for the image, add -6 to the x-coordinates of the preimage, and add to the y-coordinates of the preimage. To find the y-coordinates for the image, add to the y-coordinates of the preimage. To find the y-coordinates for the image, add to the y-coordinates of the preimage. PTS: 1 IF: verage REF: Page 51 OJ: Translations in the oordinate Plane NT: 1.3..c ST: GE.0 TOP: 1-7 Transformations in the oordinate Plane KEY: transformations arrow notation translations 8

15 I: 13. NS: Subtract from 180º and simplify. 180 (8z + 10) = 180 8z 10 = (170 8z) orrect! The measures of supplementary angles add to 180 degrees. Supplementary angles are angles whose measures have a sum of 180 degrees. Find the measure of a supplementary angle, not a complementary angle. PTS: 1 IF: verage REF: Page 9 OJ: 1-4. Finding the Measures of omplements and Supplements NT: g ST: 6MG. TOP: 1-4 Pairs of ngles KEY: complementary angles supplementary angles 14. NS: Step 1 Let the coordinates of N equal (x, y). Step Use the Midpoint Formula. Ê Ê Ë Á 1, ˆ = x + x 1 y 1 + y ˆ Ê, Ë Á = Ë Á Step 3 Find the x- and y-coordinates. 6 + x, 6 + y 1 = 6 + x = 6 + y Set the coordinates equal. Ê ( 1) = 6 + x ˆ Ê ( ) = 6 + y ˆ Ë Á Ë Á Multiply both sides by. = 6 + x 4 = 6 + y Simplify. x = 8 y = 10 Solve for x or y, as appropriate. The coordinates of N are (8, 10). ˆ orrect! Let the coordinates of N be (x, y). Substitute known values into the Midpoint Formula to solve for x and y. This is the midpoint of line segment M. If M is the midpoint of line segment N, what are the coordinates of N? Let the coordinates of N be (x, y). Substitute known values into the Midpoint Formula to solve for x and y. PTS: 1 IF: verage REF: Page 44 OJ: 1-6. Finding the oordinates of an Endpoint NT: 1..1.e ST: GE17.0 TOP: 1-6 Midpoint and istance in the oordinate Plane KEY: midpoint formula coordinates 9

16 I: 15. NS: Step 1 Write an equation and solve. JK = KL K is the midpoint of JL. 6x = 3x + 3 Substitute 6x for JK and 3x + 3 for KL. 3x = 3 Subtract 3x from both sides. x = 1 ivide both sides by 3. Step Find JK, KL, and JL. JK = 6x = 6( 1) = 6 KL = 3x + 3 = 3(1) + 3 = 6 JL = JK + KL = = 1 This is the value of x. Substitute this value for x to solve for the segment lengths. orrect! Reverse your answers. The first two segments are half as long as the last segment. heck your simplification methods when solving for x. Use division for the last step. PTS: 1 IF: verage REF: Page 16 OJ: 1-.5 Using Midpoints to Find Lengths NT: 1..1.e ST: GE1.0 TOP: 1- Measuring and onstructing Segments KEY: midpoints length 10

17 I: 16. NS: Let m = x. Then m = (90 x). m = 3m + x = 3(90 x) + Substitute. x = 70 3x + istribute. x = 7 3x ombine like terms. 4x = 7 dd 3x to both sides. x = 7 4 ivide both sides by 4. x = 68 Simplify. The measure of is 68, so its complement is. This is the original angle. Find the measure of the complement. Simplify the terms when solving. heck your equation. The original angle is degrees more than 3 times its complement. orrect! PTS: 1 IF: verage REF: Page 9 OJ: Using omplements and Supplements to Solve Problems NT: g ST: 6MG. TOP: 1-4 Pairs of ngles KEY: complementary angles supplementary angles 17. NS: If the Ybarra s current position is represented by X, then the distance they must travel before they stop for lunch is XR. SX + XR = SR XR = SR SX Segment ddition Postulate Solve for XR. XR = 1 ( 360) 55 Substitute known values. R is the midpoint of SJ, so SR = 1 SJ. XR = 15 Simplify. orrect! Use the definition of midpoint and the Segment ddition Postulate to find the distance to Roseburg. This is the distance from Springfield to Roseburg. You must subtract the distance they have already traveled. This is the distance to Junction ity. Use the definition of midpoint and the Segment ddition Postulate to find the distance to Roseburg. PTS: 1 IF: verage REF: Page 15 OJ: 1-.4 pplication NT: 1..1.e ST: GE1.0 TOP: 1- Measuring and onstructing Segments KEY: application segment addition postulate 11

18 I: 18. NS: 1 and have a common vertex,, a common side,, and no common interior points. Therefore, 1 and are adjacent angles. orrect! djacent angles form a linear pair if and only if their noncommon sides are opposite rays. Two angles are adjacent if they have a common vertex and a common side, but no common interior points. PTS: 1 IF: verage REF: Page 8 OJ: Identifying ngle Pairs NT: g ST: 6MG.1 TOP: 1-4 Pairs of ngles KEY: angle pairs linear pair adjacent 19. NS: E = + E Segment ddition Postulate 6x = ( 4x + 8) + 7 Substitute 6x for E and 4x + 8 for. 6x = 4x + 35 Simplify. x = 35 x = 35 x = 35 or 17.5 Simplify. E = 6x = 6( 17.5) = 105 Subtract 4x from both sides. ivide both sides by. You found the value of x. Find the length of the specified segment. You found the length of a different segment. orrect! heck your equation. Make sure you are not subtracting instead of adding. PTS: 1 IF: verage REF: Page 15 OJ: 1-.3 Using the Segment ddition Postulate NT: a ST: GE1.0 TOP: 1- Measuring and onstructing Segments KEY: segment addition postulate 1

19 I: 0. NS: Solve for the perimeter of the triangle. P = a + b + c Solve for the area of the triangle. = 1 bh = 6 + (x + 8) + 6x = 1 (x + 8)(6) = 7x + 14 = 3x + 4 heck your algebra when adding like terms. orrect! The triangle's area is half of its base times its height. The triangle's area is half of its base times its height. PTS: 1 IF: verage REF: Page 36 OJ: Finding the Perimeter and rea NT: 1..1.h ST: GE8.0 TOP: 1-5 Using Formulas in Geometry KEY: perimeter area triangles 1. NS: The perimeter of one rectangle is P = l + w = () + (3) = = 10 in. The total perimeter of 30 rectangles is 30(10) = 300 in. 300 in. of red thread will be needed. This is the perimeter of one rectangle. What is the perimeter of all 30 rectangles? To find the perimeter add (length) + (width). To find the perimeter add (length) + (width). orrect! PTS: 1 IF: verage REF: Page 37 OJ: 1-5. pplication NT: 1..1.h ST: GE8.0 TOP: 1-5 Using Formulas in Geometry KEY: application perimeter 13

20 I:. NS: Using the given diagram, the coordinates of T are (3, 1). The area of a triangle is given by = 1 bh. From the diagram, the base of the triangle is b = RT = 4. From the diagram, the height of the triangle is h = 4. Therefore the area is = 1 (4)(4) = 8. To find, use the istance Formula with points (1,5) and ( 3, 3). = (x x 1 ) + (y y 1 ) = ( 3 1) + ( 3 5) = = Use the distance formula to find the measurement of. The area of a triangle is one half the measure of its base times the measure of its height. The area of a triangle is one half times the measure of its base times the measure of its height. orrect! PTS: 1 IF: dvanced NT: 1..1.e ST: GE17.0 TOP: 1-6 Midpoint and istance in the oordinate Plane KEY: area distance formula triangles 3. NS: O is another name for O, O is another name for O, and O is another name for O. Thus the diagram contains three angles. What is the name for the angle that describes the change in position from point to point? orrect! ngle O is another name for angle O, and angle O is another name for angle O. What is the name for the angle that describes the change in position from point to point? Point O is the vertex of all the angles in the diagram. PTS: 1 IF: verage REF: Page 0 OJ: Naming ngles NT: 1..1.f ST: GE1.0 TOP: 1-3 Measuring and onstructing ngles KEY: naming angles NUMERI RESPONSE 4. NS: 150 PTS: 1 IF: verage NT: 1..1.f TOP: 1-3 Measuring and onstructing ngles KEY: application angle measures 5. NS: 74 PTS: 1 IF: verage NT: 1..1.f ST: 6MG. TOP: 1-4 Pairs of ngles KEY: supplementary angles complementary angles 14