Geometry Honors: Midterm Exam Review January 2018

Transcription

1 Name: Period: The midterm will cover Chapters 1-6. Geometry Honors: Midterm Exam Review January 2018 You WILL NOT receive a formula sheet, but you need to know the following formulas Make sure you memorize them!! - Distance - Midpoint - Slope - Slope-Intercept Form The exam is 1 hour and 55 minutes multiple choice questions (60 points) - 6 open ended questions (40 points) It is YOUR responsibility to properly prepare for the midterm exam. The answers and work for the review packet will be posted on the class website. Answers will not be provided in class - it is your responsibility to go online and check your work. The schedule for midterm exams is listed in the table below. Each day of exams is a half day. There is no homeroom - report directly to the first exam of the day. You will have a 10 minute break between exams. You may wish to use this time to use the bathroom or have a light snack. You will not be allowed to leave the classroom during exams. If you are absent from an exam, you must provide a doctor s note to the attendance office. Students who are absent without a note will receive an F for the midterm exam. 7:35 9:30 9:40 11:35 Tuesday January 23 rd Period 1 Period 2 Wednesday January 24 th Period 3 Period 4/5 Thursday January 25 th Period 6/7 or 7/8 Period 8/9 or 9/10 Friday January 26 th Period 11 Period 12

2 CHAPTER 1: TOOLS OF GEOMETRY 1. Which figure shows AB and point G contained in plane R? F G H J 2. Name the intersection of AE and CG. A line CD C point C B line AB D point G 3. If point P is between A and M, which is true? A PA + AM = PM C AM + PM = AP B AM + AP = PA D AP + PM = AM 4. Find the distance between A( 3, 5) and B(4, 2), to the nearest hundredth. A 6.75 B 7.62 C 8.06 D Find EF if E is the midpoint of DF, DE = 15 3x, and EF = x + 3. F 1 G 3 H 6 J 9 6. Find the coordinates of B if A has coordinates (3, 5) and Y( 2, 3) is the midpoint of AB. A B ( 7, 1) B B (3, 3) C B (5, 2) D B ( 7, 3)

3 7. Find the length of XZ if Y( 4, 4) is the midpoint of XZ and X has coordinates (2, 4). For Questions 8-10, use the figure. 8. What is another name for 2? A WYX C WXY B 3 D Y 9. Which angles form a linear pair? F 1 and 3 H 2 and 5 G 2 and 3 J 1 and Name the angle that is vertical to 3. A 1 B 2 C 3 D If m HJK = 7y 2 and m PQR = 133, find the value of y so that HJK is supplementary to PQR. F 3 G 2 H 4 J The measure of the complement of A is 185 less than two times the measure of the supplement of A. Find m A.

4 13. In the figure, QP and QT are opposite rays. Find m PQR, m RQS, and m SQT. Then classify each angle as right, acute, or obtuse. For questions 14 and 15, use the figure below. HL bisects KHI and HG and HI are opposite rays. 14. If 1 2, m KHG = 70, and m 1 = 3d + 2, find the value of d. 15. If m 2 = a + 15 and m 3 = a + 35, find the value of a so that HL HJ. 16. Which is not a polygon? F G H J 17. Name this polygon by its number of sides and then classify it as convex or concave and regular or irregular. 18. Find the length of one side of a regular hexagon whose perimeter is 75 feet. F 25 ft G ft H 15 ft J 12.5 ft 19. Find the perimeter of a regular octagon if one of its sides is x + 6 and another side is 14 x. A 4 B 40 C 8 D 80

5 CHAPTER 2: REASONING AND PROOF 1. Make a conjecture about the next letter in the sequence. L M N P Q R T Find a counterexample for the statement. Five is the only whole number between 4.5 and Which statement has the same truth value as 3 = 5? A 3 = x B AB = 3 C AB = BC D BC = 3 + x 4. Determine whether the following statement is always, sometimes, or never true. Points X, Y, and Z determine two lines. 5. If 1 2 and 2 3, then which is a valid conclusion? I m 1 = m 2 II 1 3 III m 1 + m 2 = m 3 F I, II, and III G II only H I and II J I and III For Questions 6 and 7, name the property that justifies the given statement. 6. If AB = CD and CD = 11, then AB = 11. A Transitive B Symmetric C Congruence D Reflexive 7. If XYZ PQR, then PQR XYZ. F Transitive G Symmetric H Congruence J Reflexive 8. Given: x + 3 = 15x 53 Prove: x = 4

6 9. If B is in the interior of DEF, m DEB = 27.2, and m DEF = 92.5, find m BEF. 10. If 1 is supplementary to 2 and 3 is complementary to 2, find m 3 if m 1 is 145. A 35 C 55 B 45 D Refer to the following figure to answer the questions below. a. Name a pair of supplementary angles. b. Name a pair of complementary angles. c. Find m RUV.

7 12. Given: 1 2 Prove: m ABC = 2(m 1)

8 CHAPTER 3: PARALLEL AND PERPENDICULAR LINES For Questions 1-3, use the figure below. 1. What type of angles are 3 and 10? F alternate interior angles G alternate exterior angles H corresponding angles J consecutive interior angles 2. State the transversal that forms 11 and 13. A l B m C p D q 3. If m 1 = 120, find m 8. F 60 G 110 H 120 J Find m HJK. A 33 C 78 B 45 D Find the value of x so that K l. 6. Find the value of x so that l m. 7. Two lines l and k are cut by a transversal forming two pairs of alternate interior angles: 4 and 5 and 3 and 6. Which condition below is necessary to make lines l and k parallel? F 4 3 H 4 5 and 3 6 G m 3 + m 6 = 180 J m 3 + m 6 = 90

9 8. If JK LM, then 4 must be supplementary to? 9. Given: 1 and 3 are supplementary Prove: j k 10. Find the slope of the line that passes through points A( 7, 14) and B(5, 2). F I J G J I H J I J I J 11. Find the slope of a line parallel to 3y 6x = 9.

10 12. Determine whether QR and ST are parallel, perpendicular, or neither for Q( 4, 4), R(5, 2), S(4, 5), and T(0, 1). 13. Find the distance between two lines that have equations y = 3x + 1 and y = 3x 19.

11 14. Find the distance from A( 1,5) to the line whose equation is 4x 5y = 12.

12 CHAPTER 4: CONGRUENT TRIANGLES 1. Classify DEF with vertices D(2, 3), E(5, 7) and F(9, 4). F acute G equiangular H obtuse J right 2. Find PR if PQR is isosceles, Q is the vertex angle, PQ = 4x 8, QR = x + 7, and PR = 6x In the figure, 1 2. Find the measures of the numbered angles. 4. Find m PQR. 5. If m D = 42, what is m E? A 18 C 43 B 40 D If PQ = QS, QS = SR, and m R = 20, find m PSQ.

13 7. Let ABC be an isosceles triangle with ABC PQR. If m B = 154, find m R. F 154 G 126 H 26 J If ABC WXY, AB = 72, BC = 65, CA = 13, XY = 7x 12, and WX = 19y + 34, find the values of x and y. 9. In the figure, LK bisects JKM and KLJ KLM. Determine which theorem or postulate can be used to prove that JKL MKL. 10. Which postulate or theorem can be used to prove ABD CBD? A SAS C SSS B ASA D AAS 11. Which of the following theorems can be used to prove ABC DEC? A SSS C SAS B AAS D ASA

14 12. Given: AB DE, AD bisects BE Prove: ABC DEC 13. Given: 1 2, 3 4, 5 6, 7 8 Prove: A C 14. PQR is an isosceles triangle with base QR. If m P = 6x + 40 and m Q = x 10, find x. F 20 G 25 H 30 J 100

15 15. Given: ACD is isosceles with vertex A BC DE Prove: ABE is isosceles 16. Find the coordinates of B, the midpoint of AC, if A(2a, b) and C(0, 2b). F (2a, 2b) G (a, b) H a, J U b J J U a, b 17. Write a coordinate proof showing that the segments joining the midpoints of the sides of a right triangle form a right triangle.

16 CHAPTER 5: RELATIONSHIPS IN TRIANGLES 1. In XYZ, which type of line is l? F perpendicular bisector H altitude G angle bisector J median 2. If RV is an angle bisector, find m UVT. A 10 C 68 B 34 D If BD is an altitude of ABC, find the value of x. For Questions 4 and 5, refer to the figure. 4. Find the value of a and m ZWT if ZW is an altitude of XYZ, m ZWT = 3a + 5, and m TWY = 5a Determine which angle has the greatest measure: YWZ, WZY, or ZYW. 6. In XYZ, point M is the centroid. If XM = 8, find the length of MA.

17 7. The vertices of ABC are A( 2, 3), B(4, 3), and C( 2, 3). Find the coordinates of each of the following points of concurrency of ABC. a. circumcenter b. orthocenter

18 For Questions 8 and 9 refer to the figure. 8. Which line segment is the shortest? F PQ H QR G RS J PS 9. Which line segment is the longest? A PQ B QR C RS D PS 10. Find x and the measure of each angle. Then list the sides of the triangle in order from shortest to longest. 11. Which of the following sets of numbers cannot be lengths of the sides of a triangle? A 1, 2, 3 B 2, 3, 4 C 3, 4, 5 D 4, 5, The measures of two sides of ABC are 19 and 15. The range for measure of the third side n would be 4 < n <?. 13. Determine whether 128 feet, 136 feet, and 245 feet can be the lengths of the sides of a triangle. 14. Write an inequality to describe the possible values of x. 15. Which inequality describes the possible values of x? F x > 6 H x 12 G x < 6 J 6 < x < 12

19 CHAPTER 6: QUDRILATERALS 1. Find the sum of the measures of the interior angles for a convex heptagon. 2. The measure of an interior angle of a regular polygon is 140. Find the number of sides in the polygon. 3. Which statement ensures that quadrilateral QRST is a parallelogram? A Q S C QT RS B QR TS and QR TS D m Q + m S = For parallelogram JKMH, find m JHK, m HMK, and the value of x. 5. Determine whether the vertices of quadrilateral DEFG form a parallelogram given D( 3, 5), E(3, 6), F( 1, 0), and G(6, 1).

20 6. Prove that quadrilateral PQRS is NOT a parallelogram. 7. For rectangle WXYZ with diagonals WY and XZ, WY = 3d + 4 and XZ = 4d 1, find the value of d. 8. Rectangle ABCD has vertices A( 3, 0), B( 2, 3), C(4, 1), and D(3, 2). Determine where the diagonals of the rectangle intersect. 9. If m BEC = 9z + 45 in rhombus ABCD, find the value of z. 10. In trapezoid HJLK, M and N are midpoints of the legs. Find KL.

21 11. What is the value of x? F 2 H 5.5 G 4 J What is m T in kite STVW? F 100 H 95 G 130 J JKLM is a kite. Complete each statement. a. MJ b. MK c. m L = m