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Transcript
Part I. Fill in the blank. 1. A line segment contains ______________________________________________________. 2. If AM = MB and points A, M and B are collinear, then ______________________________________________. 3. If two parallel lines are cut by a transversal, all corresponding angles are ___________. 4. If A is between B and C and are collinear, then _______________________________ . 5. A right triangle has (what types of angles?)___________________________ and ________________________ . 6. ________________________________________________ (7) are methods to prove triangles congruent. 7. The intersection of two planes is a ____________________. 8. In quadrant ___________, the x and y coordinates are both negative. 9. Acute angles measure _____________________________________. 10. Equiangular triangles are also ____________________________. 11. Parallel lines have the same _________________. 12. The intersection of two lines is a ___________________________. 13. If two angles are supplements of congruent angles, then the two angles ___________. 14. Corresponding sides of congruent triangles __________________________. 15. Skew lines are __________________________ and ___________________________ . 16. The slope of a horizontal line is _____________ . 17. Two angles are complementary if ________________________________________________________ . 18. The angles in a triangle sum to _________________ . 19. Vertical angles are ____________ and____________________________________________________________ . 20. An isosceles triangle has _________________ and ________________________________________________ . 21. An equilateral triangle has ____________________ and ______________________________________________ 22. The hypotenuse of a right triangle is opposite the ________________________________________________. 23. A(n) _____________________ of a right triangle is the longest side. 24. The slope of a vertical line is _____________________ . 25. Two lines that are not parallel or skew are _____________________ . 26. The three medians of a triangle intersect ____________________________ and _______________________. 27. When two parallel lines are cut by a transversal, the interior angles are ______________or _______________. 28. If two lines are parallel, then alternate interior angles are __________________. A Part II. Free response by chapter. True or false. B l C D Chapter 1 1. Points A, B and H are collinear. _____ 2. Point A lies on line m. _____ 3. Points B, C and H are coplanar. _____ I G H 4. Points E, J and F are collinear. _____ E 5. Point C lines on line l. ______ m J F 6. Plane ABC and plane BCF intersect at point B. _____ For questions 7 – 11, refer to the diagram at the right. 7. Name the intersection of CD and plane P. _____________ 8. If TB and TC were drawn, what would be their intersection? ______ 9. Name the intersection of line l and CD . ______________ 10. Name four noncoplanar points. _____________________ 11. Write another name for plane P. ____________________ T l A B P C D For questions 12, write the following using symbols. Do not draw. 12. a. perpendicular ________ d. parallel ________ g. ray KL ________ a. line segment AB ________ e. the length of line segment CD ________ b. angle EFG ________ f. the measure of angle HIJ _____________ 13. Find the length of the segment with endpoints H(2, 3) and J(6, 7). ____________________ 14. Find the midpoint of the segment MN with endpoints M(8, 9) and N(-2, 1). ________________ For questions 15 – 17, determine whether each statement is true of false. 15. If B is between M and T, MB = BT – MT. ________ 1 16. If C is the midpoint of AT , then CT = TA. ________ 2 17. Every segment has only one bisector. _______ 18. If m1 4 m2 , find m2 . _______ 1 2 A 2 19. Find mABC if BD bisects ABC , m1 5 x 11 and m2 3x 5. D 1 B For questions 20 – 23, refer to the figure at the right. 20. Name two right angles. __________ ___________ 21. Name two supplementary angles. . __________ ___________ 22. Name two congruent angles that are not right angles. . _____ ______ 23. Name the obtuse angle. . __________ ___________ ___________ C A 116 25 65 B 39 25 D C 24. The measure of an angle is three times the measure of its supplement. Find the measure of the angle. _____ 25. Find the value of y. ________ 3y+10 2y+20 A 2 26. Find m2 if mABC 75 and m1 16. ___________________ B 1 C 27. Find the value of x if if mABC 6x , m1 2 x 5, and m2 3x 1. ____________ Chapter 2 For questions 1 - 3, determine if the conclusion is true or false based on the given information. ABD and CBD are adjacent angles. 1. Given: _________________________________ BC and BA are opposite rays. Conjecture: ABD and CBD are supplements. PQ PR . Given: Conjecture: RPQ is a right angle. _________________________________ 3. Given: J, K and L are collinear. Conjecture: JK + KL = JL. _________________________________ 2. For questions 4 - 6, write the statement in if-then form. Underline the hypothesis once, conclusion twice. 4. Two lines intersect exactly one point. _____________________________________________________________ 5. All tigers are cats. _____________________________________________________________________________ 6. All right angles measure 90 degrees. ______________________________________________________________ Write the converse, inverse and contrapositive of the conditional statement. 7. Vertical angles are congruent. ___________________________________________________________________ Converse:______________________________________________________________________________ Inverse:________________________________________________________________________________ Contrapositive:__________________________________________________________________________ Complete the following statements. 8. A plane contains _______________________________________________________________________. 9. A line contains _______________________________________________________________________. For questions 13 – 15, name the property of equality that justifies each statement. 10. If mA mB 180 and mA 110 , then 110 mB 180 . _________________________________________ 11. If AB = CD, then CD = AB. ___________________________________________________________ 1 12. If mK mL , then 2mK mL .____________________________________________________________ 2 13. In the conditional “If p, then q”, the q is called the _____________________. 14. Find the measure of 1 . 3x+6 5x-18 1 _____________________ P Chapter 3 1. How many pairs of skew lines does the figure at the right have? ____________ A D B C Refer to the figure below. State the transversal that forms each pair of angles. Then identify the special angle pair name. l 2. 3. 4. 5. 5 and 7 __________________________ 1 and 8 __________________________ 4 and 10 _________________________ 1 and 3 __________________________ 4 B 5 3 m 2 7 1 A 8 6 11 10 9 C 6. 4 and 9 __________________________ 7. If m1 80 , m2 40 , and l m , find the angle measures. m11 _____. m3 _____, m4 _____, m5 _____, m6 _____, m7 _____, m8 _____, m9 _____, m10 _____, Find the value of x and y. 8. l m y-1 35 l ________ _________ 9. 42 3y+2 3x+1 ________ ________ m Find the value of x so that p q . 10. ________ x-5 11. 28 ________ 2x+7 2x-3 103 135 12. Tell whether a line whose slope is undefined is horizontal, vertical or neither. _______________________ 13. Find the slope of the line passing through (-3, 0) and (2, -1). __________________ 14. Find the slope of a line parallel to the line passing through (5, -3) and (8, 2). __________________ 15. Find the slope of the line perpendicular to the line passing through (4, -3) and (1, -1). ____________________ 16. Write the equation of the line with a slope of 4 passing through (-1, 3). _________________ 17. Write the equation of the line parallel to y 1 x 9 passing through (-2, 3). ______________ 2 18. Write the equation of the line perpendicular to y 1 x 1 passing through (1, 4). _____________ 3 Chapter 4 Determine whether each statement is true or false. 1. All isosceles triangles are acute. ____________ 2. An acute triangle can be equilateral. ___________ 3. A scalene triangle is never obtuse. __________ 4. A right triangle can be isosceles. __________ Use the given conditions to classify each triangle by its sides and by its angles. 5. WHO , with mW 110, WH = WO = 5 cm. ______________ ______________ 6. BAG , with mB 90, GB = 4 cm , BA = 3 cm. _______________ ______________ Find the value of x. 7. 4x-3 ________________ 5x 7x+9 8. 34 ______________ 3x+56 49 27 Write a congruence statement for the congruent triangles in each diagram. Z 9. _____________________ 10. Y _______________________ M J R X K N L P Q Determine which postulate or theorem can be used to prove the triangles congruent. 11. _______ 12. M J _________ 13. ________ B K N L A C E Always, sometimes or never. 13. An equilateral triangle is _______________ an isosceles triangle. 14. An isosceles triangle is __________ an equilateral triangle. 15. A triangle __________ has one obtuse angle and one right angle. 16. An equilateral triangle is _______________ an obtuse triangle. 17. An equilateral triangle is _______________ an acute triangle. Find the value of x and y. 18. _____ _____ 4y 70 x y 19. _____ _____ 49 20. _____ _____ X y x 24 21. What is the vertex for ABC ? ___________ Chapter 5 1. Name the triangle for which GD is a median. _________ 2. Name an altitude of A AGC . ______ D 3. Name a median to AG in E AGC . _______ 4. Name a perpendicular bisector ______ to triangle _____. 5. Name an angle bisector. _______ to angle _____ B F G C Part III: Multiple Choice Choose the best answer for each question. Chapter 1 1. Find the length of the segment with endpoints L(-1, -3) and M(-6, 9). A. 13 B. 17 C. 5 D. 12 2. Points A, B and D A. determine a plane C. are contained in only plane P B. are collinear D. are noncoplanar points F C A P E D B 3. What is the intersection of planes P and R. A points A, D and B B. AB G C. AB D. AD R 4. What is the measure of QT if R is between Q and T, QR = 14 and RT = 5? A. 10 B. 11 C. 19 D. 9 5. Find the coordinates of the midpoint of the segment with endpoints D(6, 6) and E(-2, 2). A. (3, 4) B. (2, 4) C. (4, 8) D. (1, -1) 6. What are the sides of 5 ? A. WG and WF B. AB and WF C. WB and WG D. WB and WF E B 1 8 9 C 2 7. 5 and 6 are A. adjacent 3 4 W 5 F 6 G B. vertical C. supplementary A D. complementary 7 8. 8 and 9 are A. adjacent B. vertical C. supplementary D. complementary 9. 1 and 2 are A. adjacent B. vertical C. complementary D. linear pair 10. 3 and 4 are A. adjacent B. vertical C. linear pair D. complementary 11. Find m1. A. 25 C. 175 1 B. 155 D. 5 3x+10 2x+15 12. If mABD 40 and mABC 110 , find mDBC. A. 150B. 130 C. 70 D. 80 D A B C 13. Find mRSU if ST bisects RSU , m1 4x 12 and m2 2x 6. A. 48 B. 18 C. 9 D. 24 R 1 S T 2 U Chapter 2 1. Choose the converse of “If 1 2 , then m1 = m2 . A. If m1 = m2 , then 1 2 B. If 1 2 , then 2 1 C. If m1 = m2 , then m2 = m1 . D. None of these 2. Identify the hypothesis of the statement “If today is Tuesday, then tomorrow is Wednesday.” A. Today is not Tuesday B. Today is Wednesday C. Today is Tuesday D. Tomorrow is Wednesday 3. Identify the if-then form of the following: All cars have four wheels. A. If a vehicle has four wheels, then it is a car. B. If a vehicle is a car, then it has four wheels. C. If a vehicle is not a car, then it does not have four wheels. D. None of these 4. The transitive property of equality states “If a = b and b = c, then _____ “. A. b = a B. a = c C. c = b D. b = b 7. P and Q form a linear pair and mP 62. Find mQ. A. 62 B. 28 C. 118 D. 90 Chapter 3 1. Given l m and m2 = 72, find m3 . A. 108B. 72 C. 18 D. 112 4 3 2. Given l m , m1= 9x +5 and m2 = x + 37, find the value of x. A. 32 B. 4 C. 41 D. 39 l 1 2 5 m 3. Given m4 5x 2 and m5 = 3x + 28, find the value of x so that l m . A. 26 B. 13 C. 67 D. 75 Chapter 4 1. A right triangle must be A. isosceles B. acute C. scalene D. either isosceles or scalene 2. Find the measures of the legs of an equilateral triangle PQR if PQ = 5x – 7 and PR = 2x + 5. A. 39 B. 13 C. 12 D. 4 3. In ABC , what is the angle opposite AB ? A. CA B. A C. B D. C 4. In DEF , if DE DF and EF is the hypotenuse, then DEF is A. acute and scalene B. right and scalene C. right and isosceles D. obtuse and isosceles 5. The measures of two angles of a triangle are 38 and 47. What is the measure of the third angle? A. 85 B. 95 C. 133 D. 142 6. If IGH KLJ , then H is congruent to A. J B. I C. K D. L 7. Which of the following is not a postulate used to prove the congruence of two triangles? A. ASA B. SSA C. SAS D. SSS 8. The measure of the vertex angle of an isosceles triangle is 120. That is the measure of the base angle? A. 60 B. 30 C. 35 D. 40 9. Name one additional pair of corresponding parts that need to be congruent in order to prove that T K STP MKO by ASA. A. S M B. TP KO C. T K D. ST MK S P M O C Chapter 5 1. Identify the median of ABC . A. CE B. BF C. AD D. GH G F D 2. Identify the altitude of ABC . A. CE B BF C. AD D. GH A 3. In ABC , if mABF 39 and BF is an angle bisector, find mBCE. A. 90 B. 51 C. 39 D. 12 H E B Properties State the property, theorem, postulate or definition used to make the conclusion. 1. If UV = VW, then VW = UV. ___________________________________________________ 2. If Q is a right angle, then mQ is 90 . _____________________________________________ 3. 2(x – 50) = 2x – 100. __________________________________________ 4. If 1 and 2 are vertical angles, then 1 2 . ______________________ u 5. If t u , then 2 is a right angle. _________________________ 2 6. A B C AB + BC = AC. 7. If 1 2 , then m1 m2 . 8. A A . ___________________ t __________________________________________ ______________________________________________________ ________________________________________________________________________ 9. If 2x + 4 = 17, then 2x = 13. ____________________________________________________________ 10. T is the midpoint of SR , then ST TR . ________________________________________________ 11. If 1 2 and 2 3 , then 1 3 . ________________________________________________ 12. If 3 and 4 are a linear pair, then they are supplementary. 13. If AB bisects CAD , then CAB DAB . _______________________________ ___________________________________________ 14. If 4 and 5 are supplementary, then m4 m5 180 . _____________________________________ 15. If l m , then m1 m2 180 . 16. 3 4 , then l m . _______________________________________________________ _____________________________________________________________ 3 l 1 2 4 m