Writing: Answer each question with complete sentences. 1) Explain what it means to bisect a segment. Why is it impossible to bisect a line? 2) Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain. 3) Explain why a four-legged table may rock from side to side even if the floor is level. Would a three-legged table on the same level floor rock from side to side? Why or why not? 4) Can two planes intersect in a segment? Explain. Short Answer: Answer each question completely. 5) Sketch the figure described. Three lines that lie in a plane and intersect at one point 6) Use the figure to the right to answer the following questions. a) Name the intersection of plane CDF and plane BAD. b) Are the points B and F collinear? c) Are the points B and F coplanar? d) Name three planes that intersect at point A.
7) Point S is between R and T on RT. Use the given information to write an equation in terms of x. Solve the equation. Then find RS and ST. RS = 2x + 10 ST = x 4 RT = 21 8) Point M is the midpoint of RT. Find RM, MT, and RT. 9) The endpoints of two segments are given. Find the length of the segment rounded to the nearest tenth. Then find the coordinate of the midpoint of the segment. A(2, 5) and B(4, 3) 10) Point C(3, 8) is the midpoint of AB. One endpoint is A(-1, 5). Find the coordinates of endpoint B. 11) Find m ABC and m CBD if m ABD = 120. 12) VZ bisects UVW UVW, and m UVZ o 81. Find m UVW. Then classify by its angle measure.
13) If m 2 = 6x - 1 and the m 4 = 4x + 17, then find the 3 m. 14) 1and 2 are complementary angles. Find the measures of the angles when o 1 ( x 10 and m ) o 2 (2 x 40. m ) 15) Pentagon ABCDE is a regular polygon. The length of BC is represented by the expression 5x 4. The length of DE is represented by the expression 2x + 11. Find the length of AB. 16) Draw a sketch of a concave pentagon. 17) Draw an example of a linear pair. Fill-in the blank: Fill in the blank with the most appropriate word. 18) A has a definite beginning and end. 19) A has a definite starting point and extends without end in one direction. 20) are two rays that are part of the same line and have only their endpoints in common. 21) You can use a to measure angles and sketch angles of given measure. 22) Angles with the same measure are. 23) Two angles are if and only if (iff) the sum of their degree measure is 180. 24) A regular polygon is both and. 25) Describe the pattern in the numbers. Write the next three numbers. -6, -1, 4, 9,
26) Write the if-then form, the converse, the inverse, and the contrapositive for the given statement. All right angles are congruent. If-then: Converse: Inverse: Contrapositive: 27) If you decide to go to the football game, then you will miss band practice. Tonight, you are going to the football game. Using the Law of Detachment, what statement can you make? 28) If you get an A or better on your math test, then you can go to the movies. If you go to the movies, then you can watch your favorite actor. Using the Law of Syllogism, what statement can you make? 29) Show that the conjecture is false by finding a counterexample. The sum of two numbers is always greater than the larger number. Use the diagram to write examples of the stated postulate. 30) A line contains at least two points 31) A plane contains at least three noncollinear points. 32) If two planes intersect, then their intersection is a line.
33) Sketch a diagram that represents the given information: straight angle CDE is bisected by DK. Solve the equation. Write a reason for each step. 34) -7(-x + 2) = 42 Name the property illustrated by the statement. 35) If DEF JKL, then JKL DEF 36) C C 37) If m 4 57 o, find m 1, m 2, and m 3. 1 2 4 3 38) Find the measure of each angle in the diagram. 7y - 12 4x 6y + 8 6x - 26 Short answer: Answer the following questions using complete sentences. 39) How can you show that the statement, If you play a sport, then you wear a helmet. Is false? Explain. 40) Use deductive reasoning to make a statement about the picture.
41) What is a theorem? How is it different from a postulate? 42) Explain why writing a proof is an example of deductive reasoning, not inductive reasoning. 43) Describe the relationship between the angle measures of complementary angles, supplementary angles, vertical angles, and linear pairs. 44) Complete the following proofs. a) Given : AC = AB + AB Prove: AB = BC B Statements 1. AC = AB + AB 1. Given Reasons 2. AB + BC = AC 2. 3. AB + AB = AB + BC 3. Transitive Property of Equality 4. AB = BC 4. b) Given: AB is a line segment Prove: AB AB Statements Reasons 1. AB is a line segment 1. Given 2. AB is the length of AB 2. Ruler Postulate 3. AB = AB 3. 4. AB AB 4.
c) Given: A B, B C Prove: A C Statements Reasons 1. Given 1. A B, B C 2. m A m B, m B m C 2. 3. m A m C 3. Transitive Property of Eq. 4. A C 4. 45) Complete the statement. a. 3 and are corresponding angles. b. 4 and are consecutive interior angles. c. 6 and are alternate interior angles. d. 1 and are alternate exterior angles. 46) Find the value of x. Explain your reasoning. 47) Find the value of x. Explain your reasoning. 48) Find the value of x. Explain your reasoning.
Find the value of x that makes m n. 49) 50) 51) 52) A line that intersects two other lines is a. 53) Find the values of x and y. 54) Find the values of x and y. 55) Draw a pair of parallel lines with a transversal. Identify all pairs of alternate exterior angles.
56) What angle pairs are formed by transversals? 57) Michaela was stenciling this design on her bedroom walls. How can she tell if the top and bottom lines of the design are parallel? 58) In the figure each rung of the ladder is parallel to the rung directly above it. Explain why the top rung is parallel to the bottom rung. 59) How do you find the slope of a line given the coordinates of two points on the line? 60) Find the slope of the line that passes through the points (3, 5) and (5, 6). Tell whether lines through the given points are parallel, perpendicular, or neither. Justify your answer. 61) Line 1: (1, 0), (7, 4) Line 2: (7, 0), (3, 6) 62) Line 1: (-3, 1), (-7, -2) Line 2: (2, -1), (8, 4) 63) Graph the line through the given point with the given slope. P(3, -2), slope: -3
64) Write an equation of the line in slope-intercept form passing through the point (2, -3) that is parallel to the line with the equation y = 6x + 4. 65) Write an equation of the line in slope-intercept form passing through the point (3, -4) that is perpendicular to the line with the equation 1 y x 1. 2 66) What does intercept means in the expression slope-intercept form? Use complete sentences. 67) Graph the equation 2x + 3y = 12 by finding the x- and y- intercepts. 68) The segment is the shortest distance between a point and a line. 69) In the diagram, AB BC. Find the value of x. 70) Find the measure of the indicated angle. a) Angle 2 b) Angle 5 c) Angle 3
71) Complete the proof. o Given: m 1 115, m 2 65 Prove: m n o 1 2 m n 72) Can a right triangle also be obtuse? Explain why or why not. 73) What must be true of a transformation for it to be a rigid motion? 74) List three examples for transformations that are rigid motions. 75) How can you use side lengths to prove triangles congruent? 76) A triangle with three congruent sides is called. 77) Describe the difference between isosceles and scalene triangles. 78) Compare vertex angles and base angles. 79) Sketch an acute scalene triangle. Label its interior angles 1, 2, and 3. Then draw and shade its exterior angles. Find the value of x. Then classify the triangle by its angles. 80)
81) 82) 83) In the diagram, QRS XYZ 84) Find m R 85) Find XY 86) Find m X 87) Find m S 88) Write all the congruence statements for the figures. 89) Identify the transformation you could use to move the solid figure onto the dashed figure.
90) Find the values of x and y. A B C D E F G H 91) The picture below shows a gate from Fort Meigs Museum in Perrysburg, Ohio. Using what you have learned in this chapter, explain why the builder would put in the diagonal crosspiece on the gate. 92) GIVEN: M N PQ, M Q N P PROVE: MNQ PQN 93) Explain the difference between proving triangles congruent using the ASA and AAS Congruence Postulates. 94) You know that a pair of triangles has two pairs of congruent corresponding angles. What other information do you need to show that the triangles are congruent? 95) How can you use congruent triangles to prove angles or sides congruent?
96) The angle between two sides of a triangle is called the angle. 97) Corresponding parts of congruent triangles are. Use the given information to name two triangles that are congruent, if possible. Explain your reasoning. 98) RSTUV is a regular pentagon. T S U R V 99) Q U D A 100) B 101) A A D T C P R S 102) A T M H
103) Prove that RST TUR. S T R U 104) Prove that ABC DBC B. A C D 105) Given: AC R 4 AR and 1 2 C A 2 3 S Prove: 3 4 1 L 106) Given: BU UG ; UM bi sec ts BG U Prove: BUM MUG B M G 107) Given: B is the midpoint of CD ; 1 C 2 1 Prove: A E B E 2 D A