Geometry. Midterm Review

Transcription

1 Geometry Midterm Review

2 Class: Date: Geometry Midterm Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1 A plumber knows that if you shut off the water at the main valve, it is safe to remove the sink faucet. The plumber turns the main valve to the off position. What conclusion can the plumber make? A It is not safe to remove the sink faucet. B C D It is safe to remove the sink faucet. The water is not shut off. The main valve is now on. 2 How would you classify pairs of opposite angles in a parallelogram? F complementary H congruent G supplementary J adjacent 3 If the figure below is a parallelogram, what is the relationship between angles 1 and 2? A adjacent C supplementary B complementary D vertical 4 What is the measure of an exterior angle of a regular twelve-sided polygon? F 168 G 150 H 30 J 12 5 What is the sum of the measures of the interior angles of a 14-sided polygon? A 1,980 B 2,160 C 2,520 D 2,880 1

3 6 What are the measures of the interior angles of the polygon shown? F m D = 90, m E = 90, m F = 90, m G = 90 G m D = 90, m E = 60, m F = 120, m G = 60 H m D = 90, m E = 45, m F = 90, m G = 45 J m D = 90, m E = 67.5, m F = 135, m G = In ΔABC below, if m ACD = 50, what can you conclude about m A? Which method can be used to solve the problem? A B C D m A > 50; Triangle-Angle Sum Theorem m A = 50; Exterior Angle Theorem m A < 50; Exterior Angle Theorem m A = 40; Exterior Angle Theorem 8 Below is a regular octagon. What is the value of x? F 1440 H 135 G 1080 J 90 2

4 9 Rita is creating an abstract design that includes the figure below. She knows that PQR TSR. What additional information would she need to prove that TSR using ASA? A QPR SRT B C D QP ST PR TR QR SR PQR 10 The figure below shows the preliminary layout of four land plots adjacent to Broward and Florida Streets. Plot B and Plot C are congruent. A buyer wants to purchase Plot B. She wants to put a fence around the plot until construction begins. What is the perimeter of Plot B? F G H J yards 146 yards yards yards 3

5 11 Suppose CDEF represents the wing you built as part of the reconstruction of a vintage airplane model. CF is to be attached to the plane with CD closest to the propeller. You friend will build the second wing, TQRS, congruent to CDEF, but needs instructions for how to place their wing exactly like you did. What are your instructions? A B C D Attach QR to the plane with SR closest to the propeller. Attach QR to the plane with TQ closest to the propeller. Attach TS to the plane with TQ closest to the propeller. Attach TS to the plane with SR closest to the propeller. 12 Which of the following diagrams shows a parallelogram? F G H J 4

6 13 Find the values of the variables in the parallelogram. The diagram is not to scale. A x = 49, y = 29, z = 102 C x = 49, y = 49, z = 131 B x = 29, y = 49, z = 131 D x = 29, y = 49, z = Given that RSTV is a parallelogram, what are the values of x and y? F x = 24, y = 24 G x = 30.5, y = 11 H x = 34, y = 18 J x = 54, y = Which parallelograms have congruent diagonals? A rhombuses or squares B rhombuses or rectangles C rectangles or kites D rectangles or squares 5

7 16 Quadrilateral LMNO is a rhombus. What is m PLM? F 160 H 100 G 120 J QRST it an isosceles trapezoid and m R = 116. What are m S, m Q, and m T? A m S = 64, m Q = 64, m T = 116 C m S = 64, m Q = 64, m T = 64 B m S = 116, m Q = 64, m T = 64 D m S = 116, m Q = 116, m T = 116 6

8 18 Can you conclude that the parallelogram is a rhombus, a rectangle, or a square? What else is a valid conclusion and explanation? F G Square; by ASA and the converse of the Isosceles Triangle Theorem, all four sides are congruent, so the figure is a square. Rhombus; by ASA and the converse of the Isosceles Triangle Theorem, all four sides are congruent. H J Rectangle; the diagonal bisects a pair of opposite angles, so the figure is a rectangle Also, by SAS and the converse of the Equilateral Triangle Theorem, all four sides are congruent. Rhombus; the diagonal bisects a pair of opposite angles, so the figure is a rhombus Also, by SAS and the converse of the Equilateral Triangle Theorem, all four sides are congruent. 19 ABCD is a rhombus. How do you complete the explanation that states why ΔABC ΔCDA? AB CD and BC DA by the definition of rhombus. AC AC by the Reflexive Property of Congruence, so ΔABC ΔCDA by. A ASA C SAS B AAS D SSS 7

9 20 Look at parallelogram ABCD below. How could you prove that ABCD is a rhombus? F Show that the diagonals are perpendicular. G H J Show that the diagonals are congruent. Show that both pairs of opposite angles are congruent. Show that both pairs of opposite sides are congruent. 8

10 21 What is the missing reason in the proof? Given: JKLM is a parallelogram. Prove: J L Statements Reasons 1. JKLM is a 1. Given parallelogram. 2. KL Ä JM 2. Definition of a parallelogram 3. J and K are 3.? supplementary. 4. JK Ä ML 4. Definition of a parallelogram 5. L and K are 5. (Same as step 3.) supplementary. 6. J L 6. J and L are supplements of the same angle. A B C D Same-Side Interior Angles Theorem Corresponding Angles Theorem Same-Side Exterior Angles Theorem Triangle Angle-Sum Theorem 22 Where can the incenter of a triangle be located? I. inside the triangle II. on the triangle III. outside the triangle F I only G III only H I or III only J I, II, or II 9

11 23 Which of the following is an illustration of a median? A C B D 24 In the figure, XW is the perpendicular bisector of YZ, ZY = 11g, and XY = 20g. which expression represents the length of XZ? F 20g G 11g H 10g J 5.5g 10

12 25 Which congruence postulate or theorem can be used to prove the triangles below are congruent? A SSS C ASA B SAS D SSA 26 If ΔMNO ΔPQR, which of the following can you NOT conclude as being true? F MN PR G M P H NO QR J N Q 27 R, S, and T are the vertices of one triangle. E, F, and D are the vertices of another triangle. m R = 60, m S = 80, m F = 60, m D = 40, RS = 4, and EF = 4. Are the two triangles congruent? Why or why not? If yes, which segment is congruent to RT? A B C D yes, by ASA; FD yes, by AAS; ED yes, by SAS; ED No, the two triangles are NOT congruent. 28 What other information is needed in order to prove the triangles congruent using the SAS Congruence Postulate? F BAC DAC H AB Ä AD G AC BD J AC BD 11

13 29 What are the missing reasons in the two-column proof? Given: Q T and QR TR Prove: PR SR Statement 1. Q T and QR TR Reasons 1. Given 2. PRQ SRT 2. Vertical angles are congruent. 3. ΔPRQ ΔSRT 3.? 4. PR SR 4.? A ASA; Substitution C AAS; Corresp. parts of Δ are. B SAS; Corresp. parts of Δ are. D ASA; Corresp. parts of Δ are. 30 What is the correct order of the sides of the triangle from longest to shortest? F LN, LM, MN H LN, MN, LM G LM, MN, LN J MN, LN, ML 12

14 31 Which angle has the greatest measure? A B C D What is the smallest angle of ΔABC? F G H J Two angles are the same size and smaller than the third. B A C 33 Which three lengths could be the lengths of the sides of a triangle? A 12 centimeters, 5 centimeters, 17 centimeters B 10 centimeters, 15 centimeters, 24 centimeters C 9 centimeters, 22 centimeters, 11 centimeters D 21 centimeters, 7 centimeters, 6 centimeters 34 Two sides of a triangle have lengths 6 and 17. Which inequality represents the possible lengths, x, for the third side? F 11 x < 23 H 11 < x 23 G 11 x 23 J 11 < x < 23 13

15 35 How would you complete the two-column proof? Given: m 1 m 2, m 1 = 130 Prove: m 3 = 130 Drawing not to scale 1 2, m 1 = 130 m 2 = 130 Given Substitution Property m 2 = m 3? m 3 = 130 Substitution Property A Alternate Interior Angles Theorem B Substitution Property C Vertical Angles Theorem D Given 36 What would you fill in the blank to complete the proof? Given: 7y = 8x 14; y = 6 Prove: x = 7 7y = 8x 14; y = 6 Given 42 = 8x 14 Substitution Property 56 = 8x? 7 = x Division Property of Equality x = 7 Symmetric Property of Equality F Given G Addition Property of Equality H Subtraction Property of Equality J Division Property of Equality 14

16 37 What would you fill in the blank to complete the proof? Given: SV Ä TU and ΔSVX ΔUTX Prove: VUTS is a parallelogram Because ΔSVX ΔUTX, SV TU because corresponding parts of congruent triangles are congruent. It is given that SV Ä TU. Therefore quadrilateral VUTS is a because if one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram. A rectangle C rhombus B square D parallelogram 38 What is the distance between the two points in simplest radical form? G(1, 3) and J(2, 8) F 130 G 2 13 H 6 J The vertices of ΔTVS are T(1,1), V(4,0), and S(3,5). Is the triangle scalene, isosceles, equilateral, or acute? A scalene C equilateral B isosceles D acute 15

17 40 Abigail knows that the figure below is a regular pentagon with a perimeter of 70 centimeters. What is the value of x? F 10 centimeters H 14 centimeters G 12 centimeters J 16 centimeters 41 B is the midpoint of AC and D is the midpoint of CE. What is the value of x, given BD = 5x + 3 and AE = 4x + 18? A x = 2 C x = 15 B x = 7 3 D x = 21 16

18 42 What is the converse of the following conditional? If a point is in the first quadrant, then its coordinates are positive. F If a point is in the first quadrant, then its coordinates are positive. G H J If a point is not in the first quadrant, then the coordinates of the point are not positive. If the coordinates of a point are positive, then the point is in the first quadrant. If the coordinates of a point are not positive, then the point is not in the first quadrant. 43 Write a conditional statement from the following statement: A horse has 4 legs. A B C D If it has 4 legs, then it is a horse. Every horse has 4 legs. If it is a horse, then it has 4 legs. It has 4 legs and it is a horse. 44 How do you write the inverse of the conditional statement below? If m 1 = 60, then 1 is acute. F If m 1 = 60, then 1 is not acute. G If 1 is not acute, then m H If 1 is acute, then m 1 = 60. J If m 1 60, then 1 is not acute. 17

19 45 Which of the following must be true? The diagram is not to scale. A AC < FH C AB < BC B BC < FH D AC = FH 46 If m DBC = 92, what is the relationship between AD and CD? F AD < CD H AD = CD G AD > CD J not enough information 47 Find m P. The diagram is not to scale. A 50º B 60º C 40º D 130º 18

20 48 Which lines are parallel if m 3 = m 6? Justify your answer. F G H J r Ä s, by the Converse of the Same-Side Interior Angles Theorem r Ä s, by the Converse of the Alternate Interior Angles Theorem l Ä m, by the Converse of the Alternate Interior Angles Theorem l Ä m, by the Converse of the Same-Side Interior Angles Theorem 49 T(8, 15) is the midpoint of CD. The coordinates of D are (8, 20). What are the coordinates of C? A (8, 17.5) B (8, 30) C (8, 10) D (8, 25) 50 In the figure below, NP is the altitude drawn to the hypotenuse of MNO. If NP = 9 and MP = 15, what is the length of OP? F 7.2 G 6.2 H 5.4 J 4.8 Short Answer 51 What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 53? 19

21 Geometry Midterm Review Answer Section MULTIPLE CHOICE 1 ANS: B STA: MA.912.D ANS: H STA: MA.912.G ANS: C STA: MA.912.G ANS: H STA: MA.912.G ANS: B STA: MA.912.G ANS: J STA: MA.912.G ANS: C STA: MA.912.G ANS: H STA: MA.912.G ANS: D STA: MA.912.G ANS: G STA: MA.912.G ANS: C STA: MA.912.G ANS: H STA: MA.912.G ANS: D STA: MA.912.G.3.1 MA.912.G.3.2 MA.912.G.3.4 MA.912.G ANS: H STA: MA.912.G ANS: D STA: MA.912.G ANS: G STA: MA.912.G ANS: B STA: MA.912.G ANS: G STA: MA.912.G ANS: D STA: MA.912.G ANS: F STA: MA.912.G ANS: A STA: MA.912.G ANS: F STA: MA.912.G ANS: C STA: MA.912.G ANS: F STA: MA.912.G ANS: B STA: MA.912.G ANS: F STA: MA.912.G ANS: A STA: MA.912.G ANS: G STA: MA.912.G ANS: D STA: MA.912.G ANS: H STA: MA.912.G ANS: C STA: MA.912.G ANS: H STA: MA.912.G ANS: B STA: MA.912.G.4.7 1

22 34 ANS: J STA: MA.912.G ANS: C STA: MA.912.G ANS: G STA: MA.912.G ANS: D STA: MA.912.G ANS: J STA: MA.912.G ANS: A STA: MA.912.G ANS: G STA: MA.912.G ANS: A STA: MA.912.G ANS: H STA: MA.912.D.6.2 MA.912.D ANS: C STA: MA.912.D ANS: J STA: MA.912.D ANS: A STA: MA.912.G ANS: F STA: MA.912.G ANS: A STA: MA.912.G ANS: G STA: MA.912.G.1.3 MA.912.G ANS: C STA: MA.912.G ANS: H STA: MA.912.G.5.2 SHORT ANSWER 51 ANS: 74 2