Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1

Transcription

1 Name: Class: Date: Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER Multiple Choice. Identify the choice that best completes the statement or answers the question.. Which statement(s) may be true about the two lines shown in the diagram? I. The lines are coplanar. II. The lines are parallel. III. The lines intersect in one point. a. I only b. I and II only c. II and III only d. I and III only 2. Which of the following statements is false? 3. Given BAD, and a third ray AC in the interior of BAD, if m BAC = 29 and m CAD = 5 then the two angles are?. a. supplementary b. complementary c. a linear pair d. supplementary and a linear pair 4. If an obtuse angle is bisected, the resulting angles are. a. always acute b. right angles c. never congruent d. always obtuse 5. Name three points that are collinear. a. A, B, C, and D are coplanar. b. A, B, and D are collinear. c. BE and BA are opposite rays. d. Answers B and C only a. points T, Q, and R b. points T, Q, and S c. points S, Q, and R d. points T, S, and R Short Answer 6. BD 7. Find the values of the variables. bisects ABC. Find the value of x.

2 Name: 8. Find the coordinates of the midpoint of a segment with the given endpoints. Find the length of the segment. Round decimals to the nearest tenth. 4. If angle ROS is acute and angle TOR is straight, then angle TOS is what kind of angle? EÊ Ë Á 4, 8 ˆ, F Ê Ë Á 6, 6 ˆ Tell whether the polygon is best described as equiangular, equilateral, regular, or none of these. 5. Use the diagram to name the intersection of plane LMN and plane QLS Given: Area of a triangle A = 5ft 2, andbaseb = 5ft.Find the height h. 2. Find the length of CD. 3. A and B are supplementary. The measure of B is three times the measure of A. Find m A and m B. 2

3 Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER Answer Section MULTIPLE CHOICE. D 2. C 3. D 4. A 5. A SHORT ANSWER x = 25; y = (-,-); about 7.2 units 9. regular 0. equilateral. 6 ft m A = 45? m B = obtuse 5. QL

4 Name: Class: Date: Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 2 Multiple Choice. Identify the choice that best completes the statement or answers the question.. What is the next number in the pattern 3, 7 2, 4, 9 2,...? 6. In the diagram, 2. Which of the following is not true? a. -3 b. -5 c. 2 d What is the converse of "If it is raining, then we will not go to the beach?" a. If it is not raining, then we will go to the beach. b. We will go to the beach if and only if it is not raining. c. If we go to the beach, then it is not raining. d. If we do not go to the beach, then it is raining. 3. "If AB + BC = 24 and AB = 0, then 0 + BC = 24" is an example of the?. a. Symmetric property of equality b. Substitution property of equality c. Addition property of equality d. Subtraction property of equality 4. Two angles 3 and 5 are each supplementary to 4. If m 5 is 78, what is m 3? a. 02 b. 2 c. 78 d Which statement about the conditional statement "If two different lines intersect, then their intersection is a point" is true? I. The converse is true. II. The statement can be written as a true biconditional. III. The statement is false. a. I only b. I and II only c. II and III only d. III only a. 3 4 b. m 7 + m 2 + m 4 = 80? c. m 3 + m 5 = m 4 d Which inverse of the following statements is true? a. If two lines intersect to form a right angle, then they are perpendicular lines. b. If m W is less than 45, then W is acute. c. If point K is the midpoint of JL, then points J, K, and L are collinear. d. If two rays are opposite rays, then they have a common endpoint. 8. Decide which one of the following statements is false. a. Three noncollinear points determine a plane. b. A line contains at least two points. c. Through any two distinct points there exists exactly one line. d. Any three points lie on a distinct line. 9. Which of the following is an example of the Transitive Property? a. If y = x 4, then x 4 = y. b. x 3 = x 3 c. If x = 3, then x 4 = 3 4. d. If x 3 = y and y = 4, then x 3 = If PQ = 3 and PQ + RS = 5, then 3 + RS = 5 is an example of the. a. Substitution Property of Equality b. Multiplication Property of Equality c. Transitive Property of Equality d. Reflexive Property of Equality

5 Name:. Identify the property of congruence. If Q R, then R Q. a. Symmetric Property of Congruence c. Transitive Property of Congruence b. Substitution Property d. Reflexive Property of Congruence 2. In the figure shown, m AED = 04. Which of the following statements is false? a. AEB and DEC are congruent angles. c. m AEB = 86 b. m BEC = 04 d. BEC and CED are adjacent angles. Short Answer 3. Predict the next three numbers:, 5, 23, 35, and 2 form a linear pair. If m 2 = 67, what is m? 5. and 2 are supplementary angles. and 3 are vertical angles. If m 2 = 72, what is m 3? Write the inverse, converse, and contrapositive of the conditional statement. 24. If the point is on the line, then it is in the plane. Inverse: Complete with Sometimes, Always, or Never. 6. One plane passes through three noncollinear points. 7. A line contains at least two points. 8. Two distinct points are connected by two distinct lines. 9. A line passing through two distinct points in one plane lies completely in that plane. 20. Two distinct planes intersect in a pair of lines. 2. If two distinct lines intersect, their intersection is one point. 22. Through any three distinct points there exists exactly one line. 23. Skew lines intersect in exactly one point. Converse: Contrapositive: 2

6 Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 2 Answer Section MULTIPLE CHOICE. B 2. D 3. B 4. C 5. B 6. A 7. A 8. D 9. D 0. A. A 2. C SHORT ANSWER 3. 5, 7, always 7. always 8. never 9. always 20. never 2. always 22. sometimes 23. Point, Line, and Plane Postulates do not address this topic directly. 24. Inverse: If the point is not on the line, then it is not in the plane. Converse: If the point is in the plane, then it i s on the line. Contrapositive: If the point is not in the plane, then it is not on the line.

7 Name: Class: Date: Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 3 Multiple Choice Identify the choice that best completes the statement or answers the question.. In the figure, l Ä n and r is a transversal. Which of the following is not necessarily true? 2. In the figure shown, HC Ä GD and m ABC = 00? Which of the following statements is false? a. 8 2 b. 2 6 c. 5 3 d. 7 4 a. m CBE = 80 b. m DEF = 80 c. DEB and CBE are corresponding angles. d. CBE and GEB are alternate interior angles. Completion. Complete each statement. Use the diagram to complete the statement with corresponding, alternate interior, alternate exterior, or consecutive interior. 6. 4and 5 are angles. 7. 3and 7 are angles. Use the diagram to state whether the given angles are supplementary or congruent. 3. 3and 5 are angles. 4. 2and 7 are angles. 5. 2and 6 are angles. 8. 2and 6 are angles. 9. 3and 5 are angles.

8 Name: Short Answer 0. Find the slope of the line that contains each pair of given points: (5, 2), ( 8, 3) State the postulate or theorem you would use to prove that lines a and b are parallel.. Write an equation for each line that contains (4, 5) and has slope Write an equation for each line that has y-intercept 3 and slope Write an equation of the line that passes through the point P and is parallel to the line with the given equation: P(2, 6); y = 2x + 4. Write an equation of the line that passes through the point P and is perpendicular to the line with the given equation: P(5, 3); y = 5x a Ä c and b Ä c Find the value of x Write an equation of the line shown Graph the equation 5x 7y = 35. True or False: 8. If two parallel lines are intersected by a transversal, then alternate interior angles have measures of 90 degrees. 9. If two parallel lines are intersected by a transversal, then consecutive interior angles are supplementary. 24. In the figure below, if l and k are parallel lines, what is the value of x y? 2

9 Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 3 Answer Section MULTIPLE CHOICE. D 2. C COMPLETION 3. consecutive interior 4. alternate exterior 5. corresponding 6. alternate interior 7. corresponding 8. congruent 9. supplementary SHORT ANSWER y = 3x y = 3x y = 2x y = 5 x False 9. True 20. consecutive interior angles converse 2. Two lines Ä to the same line are Ä. 22. alternate interior angles converse 23. y = 2 x

10 Name: Class: Date: Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 4 Multiple Choice Identify the choice that best completes the statement or answers the question.. Which statement correctly describes the congruence of the triangles in the diagram? a. ΔABC ΔCDA d. ΔABC ΔACD b. ΔABC ΔADC e. None of these c. ΔABC ΔDCA Short Answer Decide whether it is possible to prove that the triangles are congruent. If it is possible, tell which congruence postulate or theorem you would use Find the value of x

11 Name: Would HL, ASA, SAS, AAS, or SSS be used to justify that the pair of triangles is congruent? Find the values of x and y. 9. Tell which method(s) you can use to prove that the triangles are congruent. If no method can be used, write none Use information in the figure below to find m D Line l is the perpendicular bisector of MN. 6. Find the value of x. 7. Find m M. 2

12 Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 4 Answer Section MULTIPLE CHOICE. A SHORT ANSWER 2. yes; SSS Postulate 3. yes; HL Theorem 4. no 5. yes; SAS Postulate 6. yes; AAS 7. yes; SAS 8. yes; SSS 9. Yes; SSS, reflexive property and three pairs of corresponding sides are congruent x = 2? y = ? 8. AAS 9. ASA 20. HL 2. HL 22. AAS

13 Name: Class: Date: Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 5 Multiple Choice. Identify the choice that best completes the statement or answers the question.. Which of the following statements is false? I. Medians intersect inside a triangle. II. Perpendicular bisectors intersect inside a triangle. III. Angle bisectors intersect inside a triangle. a. I only b. II only c. III only d. II, III 2. Given: BC is the perpendicular bisector of KM. Which statement is true? a. C is the midpoint of KM c. KBM is a right angle. b. CM = BM d. BLM, MLC, CLK, KLB are all right a 3. Choose the correct statement. a. x < 0 b. 0 < x < 3 c. x > 3 d. x = 3 4. Given: AB = AD, m > m 2. Then,. a. BE > ED b. BE < ED c. AE = EC d. BE = ED Short Answer 5. Determine whether it is possible to draw a triangle with sides of the given lengths:, 2, 3 7. For the given triangle, state the relationships between AB and DF. 6. Find the value of x.

14 Name: 8. Refer to the figure below. 5. Use the graph shown. Given: AF FC ; ABE EBC Which line is a perpendicular bisector in 9. A median of ABC is. 0. An altitude of ABC is. ABC?. The medians of a triangle are concurrent. Their common point is the. Find the coordinates of D, the midpoint of AC. Use the median BD to find the coordinates of the centroid P. 6. Refer to the figure. The longest segment is. 2. Refer to the figure below. 7. Refer to the figure. What is the largest angle that is part of a triangle in the figure? a. If BC = 5, then LN =. b. If AB = 3x + 5 and NM = 2x +, then NM =. 3. In the diagram, X is the incenter of ΔRTV. Find XU. 8. Given: D is the circumcenter. Find BD. 4. Given: V is the centroid of ΔRST, SU RT, UT = 2, RW = 7.5, SV = 6. Find ST and UV. 2

15 Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 5 Answer Section MULTIPLE CHOICE. B 2. D 3. C 4. A SHORT ANSWER 5. No AB Ä DF and AB = 2 DF 8. GF 9. BF 0. BD. centroid 2. a. 7.5 b XU = ; 3 5. DÊ Ë Á 5, 0 ˆ ; P Ê Ë Á 5, 2 ˆ 6. ML 7. ACD 8. 2

16 Name: Class: Date: Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 6 Multiple Choice. Identify the choice that best completes the statement or answers the question.. Which of the following pairs of numbers has a geometric mean of 44? a. 3 and 72 b. 40 and 48 c. 6 and 2 d. 2 and The triangles shown are similar. Which of the following is not a correct statement? a. AB XY = BC YZ b. ΔABC ΔXYZ c. BC YZ = AC XY d. CA ZX = BA YX 3. The distance between two cities on a map is 7 centimeters. The map has a scale of cm : 20 km. Find the actual distance between the two cities. a km b cm c km d. 40 km 4. If a b = x, then which one of the following is not y necessarily true? a. ay = bx b. a + x b + y = a b + x y c. b a = y x d. y b = x a Short Answer 5. Solve: x Complete. = Distance Across a Ravine Use the known distances in the diagram to find the distance across a ravine from Z to Y. 6. If 5 3 = s t, then t 3 =?. 7. If 2 9 = m n, then 9 2 =?. 8. If 5 p = 4 q, then 5 + p p =? q. 0. The two polygons are similar. Find x. Then find the scale factor and the ratio of the perimeters. A(-6, 2), B(2, 2), C(2, 0), D(-6, 0); k = 0.5

17 Name: For the next four problems, use the diagram. Given: ABCD WXYZ. Are the triangles similar? If so, state the similarity and a postulate or theorem that can be used to prove that the triangles are similar. 7.. Find the scale factor of WXYZ to ABCD Find the values of s, t, and u. 3. Find the perimeter of each polygon. 4. Find the ratio of the perimeter of ABCD to the perimeter of WXYZ Use the diagram. CD AD =?? Use the diagram to find x The two polygons are similar. Find x. Then find the scale factor and the ratio of the perimeters. 2. 2

18 Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 6 Answer Section MULTIPLE CHOICE. C 2. C 3. D 4. B SHORT ANSWER 5. 2 s 6. 5 n 7. m q yds 0. Ê Ë Á 3, ˆ, Ê Ë Á, ˆ, Ê Ë Á, 0ˆ, Ê Ë Á 3, 0 ˆ s = 4.5, t = 6, u = 0 3. ABCD: 2; WXYZ: :2 ED 5. GD 6. ; 2:3; yes; ΔGHI ΔKJL; SAS Similarity 8. yes; ΔMON ΔQOP; AA Similarity 9. yes; ΔRSV ΔUTV; AA Similarity