Semester 1 Cumulative Summative Review Teacher: Date: B

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1 GOMTRY Name: Semester 1 umulative Summative Review Teacher: ate: To be prepared for your midterm, you will need to PRTI PROLMS and STUY TRMS from the following chapters. Use this guide to help you practice along with notes, old assessments, and leks. hapter 1 ( ): Points Lines and Planes Segments and ongruence Midpoint and istance Formulas Measure and lassify ngles escribe ngle Pair Relationships hapter 2: onditional Statements (onverse, Inverse, ontrapositive, iconditional) Postulates and iagrams Reasoning Properties from lgebra Proving Geometric Statements hapter 3 ( ): Parallel Lines and ngle Relationships (orresponding, onsecutive, lternate Interior/xterior) Perpendicular Lines Find and Use Slopes of Lines Write and Graph quations of Lines hapter 4 ( ): Triangle lassification (cute, Obtuse, Right, quiangular, quilateral, Scalene, Isosceles) Triangle Sum Properties Triangle ongruence (SSS, SS, S, S, HL) Isosceles and quilateral Triangle Properties hapter 5 ( ): Inequalities in a Triangle Relationships etween Side Lengths and ngle Measures Inequalities in Two Triangles (Hinge Theorem) hapter 6: Ratios, Proportions, Geometric Mean Prove Triangles Similar (, SSS, SS) Use Proportionality Theorems

2 Geometry Name: Midterm Review Period: ate: 1) Ray PR is shown in which sketch? a) b) c) d) P P Q Q R R P Q R R Q P 2) Use the Segment ddition Postulate to solve for p. F = 4p + 20 G = 5p + 16 FG = 45 a) p = 1 b) p = 4 c) p = 5 d) p = 6 F G 3) Find the distance between ( 6, 0) and ( 4, 4). a) 116 b) 2 5 c) 116 d) 20 4) Find the midpoint of ( 6, 0) and ( 4, 4). 5) M is the midpoint of segment. Given the coordinates of (2, 4) and M(4, 6), find the coordinates of. J 6) If m JOL = 50 and m KOL = 27, then what is the measure of JOK? a) 25 b) 23 c) 28 d) 20 O K L 7) Given that m G=60, m GF=2x + 7 and m F=7x 1, find m GF and m F. G F 8) In the figure below, m = 128. Which of the following statements is false? a) m = 128 b) and are congruent c) and are vertical angles d) m = 52

3 9) 1 and 2 are. a) a linear pair b) complementary angles c) supplementary angles d) vertical angles ) Solve for x. 5x x ) Solve for x. 5x x ) Name an angle that is adjacent to O a) O b) O c) O d) O O 13) Using the diagram, name an angle that is complementary to O. a) O b) O c) O d) O O 14) Rewrite the statement in if-then form: Vertical angles are congruent. 15) What is the converse of the statement, If it rains then I carry my umbrella.? a) If it does not rain, then I do not carry my umbrella. b) If I do not carry my umbrella, then it does not rain. c) If I do not carry my umbrella, then I will get wet. d) If I carry my umbrella, then it rains. 16) What is the inverse of the statement, If two lines are parallel, then they do not intersect.? a) If two lines are not parallel then they intersect. b) If two lines intersect then they are not parallel. c) If two lines do not intersect then they may be skew. d) If two lines do not intersect then they are not parallel. 17) Which of the following statements is false? a) Three non-collinear points determine a plane. b) ny three points are collinear. c) line contains at least two points. d) Through any two distinct points there exists exactly one line.

4 18) Rewrite the biconditional statement as a conditional statement and its converse. iconditional: Two lines are perpendicular if and only if they form four right angles. onditional: onverse: 19) Write the converse of the conditional statement and decide if the statement can be written as a biconditional. If I got a speeding ticket, then I was exceeding the speed limit. onverse: iconditional? 20) Let p represent x 2 = 21, nd let q represent x is not a whole number. Which is a representation of the statement below? If x is a whole number, then x a. ~p ~q b. ~p q c. p ~q d. ~q ~p 21) State a counterexample to the following statement: If x 2 = 25, then x = 5. a. x = 5 b. x = 5 c. x 2 = 25 d. x 2 = ) The figure at right represents which of the following statements? a) two perpendicular rays b) two perpendicular lines c) a straight angle d) = 23) Match the argument below with the type of reasoning listed. Law of Syllogism Law of etachment Neither 24) In the cube shown at right, and HG are called a) parallel lines b) perpendicular lines c) intersecting lines d) skew lines F H G

5 25) In the figure shown, 1 and 2 are a) same-side interior angles b) corresponding angles c) alternate interior angles d) alternate exterior angles 1 2 n l m 26) In the figure, 6 and 3 are ) corresponding angles ) alternate interior angles ) alternate exterior angles ) consecutive interior angles n m l 27) In the figure above, 6 and 2 are angles. 28) Find x so that a is parallel to b. x = 29) omplete the following 2-column proof: Given: JM LM & m KJM m KLM 90 Prove: JK KL Given Given 30) Write a proof of the following: Given: & Prove: Given 31) Write a proof of the following: Given: IH HK & IJ JK Prove: IHJ KHJ Given

6 32) In the figure, l n and r is a transversal. Which of the following is not necessarily true? r a) 2 6 b) 8 2 c) 7 4 d) l n 33) In the figure shown, H G, and m = 108. Which of the following statements is false? a) m F = 72 b) H and G are alternate exterior angles c) HF and are alternate interior angles d) m GF = 108 H G F 34) Find the slope of the line passing through the points (1, 6) and ( 6, 5). 35) line parallel to 2 y x 7 is: a) y x b) y x 7 c) y x 2 d) y x ) Which describes the relationship between the lines with equations 7x 6y 4 and 6x 7y 0? a) parallel b) same line c) perpendicular d) neither parallel nor perpendicular 37) lassify NOP. O a) quilateral b) Isosceles c) Scalene d) none of these ) Name an obtuse triangle in the diagram at right N 10 P ) Solve for x. 2x x ) Which figures appear to be congruent? a) 3 and 4 b) 1, 2, and 4 c) 2 and 5 d) 1 and

7 41) If XYZ, then. 42) If JKL STU, JK = 10 feet, m K = 59, and m U = 21, which of the following is false? a) JL = SU b) KL = TU c) m S = 100 d) K S 43) In the diagram, and F. Find the value of x. x F 44) What must be true for by SS? a) b) c) d) 45) Which of the following statements must be true, if and =? a) by SSS b) by SS c) by HL d) There are no congruent triangles 46) Refer to the figure at right. a) b) c) d) 47) Using just the information shown in the diagram, which postulate or theorem can be used to prove that? 48) What is the measure of each base angle of an isosceles triangle if its vertex angle measures 32 and its 2 congruent sides measure 17 inches? 49) In, if and m = 39, then m =. a) 39 b) 51 c) 102 d) ) Find the values of x and y. x a) x = 70 and y = 50 b) x = 40 and y = 110 c) x = 40 and y = 70 d) x = 70 and y = y

8 51) The longest side in the figure is N 70 a) NM b) ML c) LN d) MP L P 52) Two sides of a triangle have lengths 12 and 27. The length of the third side must be greater than and less then. a) 14, 40 b) 15, 39 c) 11, 28 d) 12, 27 M 53) Which side lengths allow you to construct a triangle? a) 7, 2, and 2 b) 2, 3, and 8 c) 1, 4, and 9 d) 6, 8, and 10 54) Lines and intersect at P. PR is perpendicular to and m P = 170. What is the measure of P? a) 10 b) 20 c) 30 d) 40 55) ladder is leaning against a house at an angle of 38, as shown in the diagram. What is the measure of the angle x, that the ladder makes with the ground? 56) Line a is parallel to line b if: a) m 4 = m 2 b) m 3 = m 5 c) m 4 = m 5 d) m 3 = m a b 57) Which conclusion follows logically from the true statements? If negotiations fail, then the baseball strike will not end. If the baseball strike does not end, then the World Series will not be played. a) If the baseball strike ends, the World Series will be played. b) If negotiations do not fail, the baseball strike will end. c) If negotiations fail, the World Series will not be played. d) If negotiations fail, the World Series will be played. 58) Given that and, which could be used to prove that? a) SSS b) SS c) S d) S

9 59) On the shores of a river, surveyors marked locations,, and. m = 70 and m = 65. Which lists the distances between these locations in order, least to greatest? 60) The figure has angle measures as shown. What is m? 61) Which of the following could be the lengths of the sides of? a) = 12, = 15, = 2 b) = 9, = 15, = 4 c) = 150, = 100, = 50 d) = 10, = 8, = 12 61) To find the contrapositive of a conditional statement you should: a) Find the inverse of the converse of the original statement. b) Find the converse of the inverse of the original statement. c) Negate the hypothesis and conclusion of the converse of the original statement. d) ll of the above. 62) Three lookout towers are located at points,, and on a section of the national forest shown in the diagram. Which of the following is true concerning formed by the towers? a) m is greatest b) m is greatest c) m is least d) m is least 63) In the figure, m is twice m. What is m? a) 120 b) 60 c) 45 d) 30 64) Triangle XYZ is a right triangle with the right angle at Z. Which are possible measures for angle X and angle Y? a) 40 and 42 b) 44 and 46 c) 48 and 50 d) 52 and 54 67) xplain the difference between similar triangles and congruent triangles. e specific. omplete the following sentences with always, sometimes, or never. 68) n isosceles triangle is a right triangle. 69) n obtuse triangle is a right triangle. 70) right triangle is an equilateral triangle. 71) right triangle is an isosceles triangle.

10 Questions 68-77: True/False, write true or false in the blank. 72) orresponding parts of congruent triangles are equal in measure. 73) oplanar points are collinear. 74) ollinear points are coplanar. 75) SS is a method to prove triangle congruency. 76) When two planes intersect, they form a line. 77) quilateral triangles are equiangular. 78) Skew lines are coplanar. 79) If two lines are parallel, they have the same slope. 80) In a right triangle, the hypotenuse is adjacent to the right angle. 81) The slope of a horizontal line is zero. 82) Simplify the following ratio as much as possible: a) 1 4 b) 4 in 1 ft 8 c) 24 8 in 2 ft d) ) Solve the proportion: x ) In the diagram ~ XYZ. Find YZ. a) 9/2 b) 2 c) 5 d) 8 85) re the two triangles in this diagram similar? If so, give the similarity statement. a) Yes, ~ b) Yes, ~ c) Yes, ~ d) No, the triangles are not similar. 86) In the diagram shown on the right, what is the length of? a) 4 b) 3/2 c) 8/3 d) 16 87) If two triangles have one pair of congruent angles and if the lengths of the corresponding adjacent sides are proportional, then the triangles are: a) equal b) congruent c) similar d) obtuse 88) The ratio of the volume of two similar rectangular prisms is 64:125. What is the ratio of the surface area?