Honors Geometry Semester Review Packet


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1 Honors Geometry Semester Review Packet 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 fourlegged table may rock from side to side even if the floor is level. Would a threelegged 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
2 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 rounding to the nearest tenth. Then find the coordinates 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) VZ bisects UVW, and m UVZ 42 o. Find m UVW. Then classify UVW by its angle measure. 12) 1 and 2 are complementary angles. Find the measures of the angles when m ) o 1 ( x 10 and m ) o 2 (2x ) 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 Find the length of AB.
3 14) Draw a sketch of a concave pentagon. 15) Draw an example of a linear pair. Fillin the blank. 16) A has a definite beginning and end. 17) A has a definite starting point and extends without end in one direction. 18) are two rays that are part of the same line and have only their endpoints in common. 19) You can use a to measure angles and sketch angles of given measure. 20) Angles with the same measure are. 21) Two angles are if and only if (iff) the sum of their degree measure is ) A regular polygon is both and. 23) Describe the pattern in the numbers. Write the next three numbers. 6, 1, 4, 9, 24) Write the ifthen form, the converse, the inverse, and the contrapositive for the given statement. All right angles are congruent. Ifthen:
4 Converse: Inverse: Contrapositive: 25) 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? 26) 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? 27) 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. 28) A line contains at least two points 29) A plane contains at least three noncollinear points. 30) If two planes intersect, then their intersection is a line. 31) Sketch a diagram that represents the given information: straight angle CDE is bisected by DK. Solve the equation. Write a reason for each step.
5 32) 7(x + 2) = 42 Name the property illustrated by the statement. 33) If DEF JKL, then JKL DEF 34) C C 35) If m 4 57 o, find m 1, m 2,and m ) Find the values of each variable and angle measure in the diagram. 7y x 6y + 8 6x ) How can you show that the statement, If you play a sport, then you wear a helmet. Is false? Explain. 38) Use deductive reasoning to make a statement about the picture. 39) What is a theorem? How is it different from a postulate? 40) Explain why writing a proof is an example of deductive reasoning, not inductive reasoning. 41) Proofs:
6 a) Given : AC = AB + AB Prove: AB = BC B Statements 1. AC = AB + AB 1. Given Reasons 2. AB + BC = AC 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 AB AB 4. 42) Complete the statement. a. 4 and are corresponding angles. b. 3 and are consecutive interior angles. c. 5 and are alternate interior angles. d. 7 and are alternate exterior angles. 43) Find the value of x. Explain your reasoning.
7 44) Find the value of x. Explain your reasoning. 45) Find the value of x. Explain your reasoning. Find the value of x that makes m n. 46) 47) 48)
8 49) A line that intersects two other lines is a. 50) Find the values of x and y. 51) Draw a pair of parallel lines with a transversal. Identify all pairs of alternate exterior angles. 52) What angle pairs are formed by transversals? 53) Michaela was stenciling this design on her bedroom walls. How can she tell if the top and bottom lines of the design are parallel? 54) 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. 55) Find the slope of the line that passes through the points (3, 5) and (5, 6).
9 56) Tell whether lines through the given points are parallel, perpendicular, or neither. Justify your answer. Line 1: (1, 0), (7, 4) Line 2: (7, 0), (3, 6) 57) Write the slopeintercept form of the equation of the line. 11x 4y = 32 58) Write the standard form of the equation of the line through the given point with the given slope. Through: (1, 2); slope = 7 59) Write an equation of the line in slopeintercept form passing through the point (3, 4) that is perpendicular to the line with the equation 1 y x ) What does intercept means in the expression slopeintercept form? Use complete sentences. 61) Explain how you can use the standard form of a linear equation to find the intercepts of a line. Use complete sentences. 62) Draw a line with an undefined slope on the coordinate plane. 63) The segment is the shortest distance between a point and a line.
10 64) In the diagram, AB BC. Find the value of x. 65) Find the distance from point A to line c. Round your answer to the nearest tenth, if necessary. 66) Can a right triangle also be obtuse? Explain why or why not. 67) What must be true of a transformation for it to be a rigid motion? 68) List three examples for transformations that are rigid motions. 69) How can you use side lengths to prove triangles congruent? 70) A triangle with three congruent angles is called. 71) Describe the difference between isosceles and scalene triangles.
11 72) Draw right isosceles triangle. 73) Draw an acute scalene triangle. Find the value of x. Then classify the triangle by its angles. 74) 75) 77) 78) 79) Find the measure of angle 1. 80) Find m JKM. 1
12 81) Write all the congruence statements for the figures. 82) Identify the transformation you could use to move the solid figure onto the dashed figure. 83) Find the values of x and y. ABCD EFGH 84) Explain why the bench with the diagonal support is stable, while the one without support can collapse. 85) Explain how you could show that the triangles are congruent in the figure.
13 86) Explain the difference between proving triangles congruent using the ASA and AAS Congruence Postulates. 87) 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? 88) Explain what CPCTC is and why is it useful? 89) The angle between two sides of a triangle is called the angle. 90) Are isosceles triangles always acute triangles? Explain your reasoning. Use the given information to name two triangles that are congruent, if possible. Explain your reasoning by stating the postulate and the congruence statements for the sides and/or angles that you used. 91) RSTUV is a regular pentagon. T S U R V 92) Q U D A 93) B A D C
14 94) A T P R S 95) A T M State the third congruence that must be given to prove that ABC DEF using the indicated postulate. Given: AB DE, CB FE, Use the SSS Congruence Postulate. Given: A D, CA FD, Use the SAS Congruence Postulate. H A B C D E F 96) Given: BC EF, B E, Use the ASA Congruence Postulate. Find the values of x and y. 97) U M 5 y o 5 3x o D 5 98) (x+7) o 55 o y o
15 99) Find the values of angles 1, 2, 3, and 4. a) Prove that RST TUR. R S U T Statements 1. Given 2. RT TR 3. RST TUR Reasons b) Prove that ABD CBD. B A D C c) Given: BU GU ; UM bisec ts BG Prove: BUM GUM Statements 1. Reasons Given 2. ADB CDB All right angles are congruent 3. reflexive 4. ABD CBD prop of congruence U
16 Statements 1. BU GU, UM bisec ts BG Reasons given 2. BM GM Definition of a bisector 3. reflexive property of congruence 4. BUM GUM B M G 5. BUM GUM E WY is the midsegment of ΔQRS. Find the value of x. 101) 102) 103) Find the value of x. 104)
17 105) In the diagram, the perpendicular bisectors of ΔWXY meet at point Z. Find the indicated measure. 106) WZ 107) ZY Find the coordinates of the centroid P of ΔSTU. 108) S(2, 5), T(5, 2), U( 1, 6) 109) S( 1, 7), T(5, 6), U( 7, 4) In ΔABC, Q is the centroid. Find the indicated length. Show your work. 110) QC = 12. Find QM. 111) QC = 6. Find CL. List the sides and the angles in order from smallest to largest. 112) 113)
18 Is it possible to construct a triangle with the given side lengths? Justify your answer. 114)10, 7, )26, 20, 2 Describe the possible lengths of the third side of the triangle given the lengths of the other two sides. 116) 5 inches, 6 inches 117) 14 feet, 21 feet Complete the statement with <, >, or =. 118) AB BC 119) RS VU 120) Suppose you wanted to prove the statement If x + y > 20 and y = 5, then x > 15. What temporary assumption could you make to prove the conclusion indirectly? Use the Hinge Theorem or its converse and properties of triangles to write and solve an inequality to describe a restriction on the value of x. 121) 122)
2) Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain.
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