Geometry Midterm Review

Name: ______________________ Class: _________________ Date: _________ ID: A

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Geometry Midterm Review

Multiple ChoiceIdentify 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 It is safe to remove the sink faucet.C The water is not shut off.D The main valve is now on.

2 How would you classify pairs of opposite angles in a parallelogram?

F complementary H congruentG supplementary J adjacent

3 If the figure below is a parallelogram, what is the relationship between angles 1 and 2?

A adjacent C supplementaryB 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 1,980B 2,160C 2,520D 2,880

Name: ______________________ ID: A

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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 = 67.5°

7 In "ABC below, if m!ACD = 50 , what can you conclude about m!A ? Which method can be used to solve the problem?

A m!A > 50; Triangle-Angle Sum TheoremB m!A = 50; Exterior Angle TheoremC m!A < 50; Exterior Angle TheoremD 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°

Name: ______________________ ID: A

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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 PQR # TSR using ASA?A !QPR # !SRTB QP # ST

C PR # TRD QR # SR

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 148.5 yardsG 146 yardsH 141.5 yardsJ 123.5 yards

Name: ______________________ ID: A

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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 Attach QR to the plane with SR closest to the propeller.B Attach QR to the plane with TQ closest to the propeller.C Attach TS to the plane with TQ closest to the propeller.D Attach TS to the plane with SR closest to the propeller.

12 Which of the following diagrams shows a parallelogram?

F

G

H

J

Name: ______________________ ID: A

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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 = 131B x = 29, y = 49, z = 131 D x = 29, y = 49, z = 102

14 Given that RSTV is a parallelogram, what are the values of x and y?

F x = 24, y = 24G x = 30.5, y = 11H x = 34, y = 18J x = 54, y = 44

15 Which parallelograms have congruent diagonals?A rhombuses or squaresB rhombuses or rectanglesC rectangles or kitesD rectangles or squares

Name: ______________________ ID: A

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16 Quadrilateral LMNO is a rhombus.

What is m!PLM?F 160° H 100°G 120° J 60°

17 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 = 64B m!S = 116, m!Q = 64, m!T = 64 D m!S = 116, m!Q = 116, m!T = 116

Name: ______________________ ID: A

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18 Can you conclude that the parallelogram is a rhombus, a rectangle, or a square? What else is a valid conclusion and explanation?

F Square; by ASA and the converse of the Isosceles Triangle Theorem, all four sides are congruent, so the figure is a square.

H 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.

G Rhombus; by ASA and the converse of the Isosceles Triangle Theorem, all four sides are congruent.

J 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 "ABC # "CDA?

AB # CD and BC # DA by the definition of rhombus. AC # AC by the Reflexive Property of Congruence, so "ABC # "CDA by _________.A ASA C SASB AAS D SSS

Name: ______________________ ID: A

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20 Look at parallelogram ABCD below.

How could you prove that ABCD is a rhombus?F Show that the diagonals are perpendicular.G Show that the diagonals are congruent.H Show that both pairs of opposite angles are congruent.J Show that both pairs of opposite sides are congruent.

Name: ______________________ ID: A

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21 What is the missing reason in the proof?Given: JKLM is a parallelogram.Prove: !J # !L

Statements Reasons1. JKLM is a

parallelogram.1. Given

2. KL Ä JM 2. Definition of a parallelogram

3. !J and !K are supplementary.

3. ?

4. JK Ä ML 4. Definition of a parallelogram

5. !L and !K are supplementary.

5. (Same as step 3.)

6. !J # !L 6. !J and !L are supplements of the same angle.

A Same-Side Interior Angles TheoremB Corresponding Angles TheoremC Same-Side Exterior Angles TheoremD Triangle Angle-Sum Theorem

22 Where can the incenter of a triangle be located?I. inside the triangleII. on the triangleIII. outside the triangleF I only G III only H I or III only J I, II, or II

Name: ______________________ ID: A

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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 20gG 11gH 10gJ 5.5g

Name: ______________________ ID: A

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25 Which congruence postulate or theorem can be used to prove the triangles below are congruent?

A SSS C ASAB SAS D SSA

26 If "MNO # "PQR, 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 yes, by ASA; FDB yes, by AAS; EDC yes, by SAS; EDD 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 ADG AC $ BD J AC # BD

Name: ______________________ ID: A

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29 What are the missing reasons in the two-column proof?Given: !Q # !T and QR # TR

Prove: PR # SR

Statement Reasons

1. !Q # !T and

QR # TR1. Given

2. !PRQ # !SRT 2. Vertical angles are congruent.

3. "PRQ # "SRT 3. ?

4. PR # SR 4. ?

A ASA; Substitution C AAS; Corresp. parts of # " are #.B SAS; Corresp. parts of # " are #. D ASA; Corresp. parts of # " are #.

30 What is the correct order of the sides of the triangle from longest to shortest?

F LN, LM, MN H LN, MN, LMG LM, MN, LN J MN, LN, ML

Name: ______________________ ID: A

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31 Which angle has the greatest measure?

A !1B !2C !3D !4

32 What is the smallest angle of "ABC?

F Two angles are the same size and smaller than the third.G !BH !AJ !C

33 Which three lengths could be the lengths of the sides of a triangle?A 12 centimeters, 5 centimeters, 17

centimetersC 9 centimeters, 22 centimeters, 11

centimetersB 10 centimeters, 15 centimeters, 24

centimetersD 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 % 23G 11 % x % 23 J 11 < x < 23

Name: ______________________ ID: A

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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° Given

m!2 = 130° Substitution Property

m!2 = m!3 ?

m!3 = 130° Substitution PropertyA Alternate Interior Angles TheoremB Substitution PropertyC Vertical Angles TheoremD 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 Given42 = 8x & 14 Substitution Property

56 = 8x ?7 = x Division Property of Equalityx = 7 Symmetric Property of Equality

F GivenG Addition Property of EqualityH Subtraction Property of EqualityJ Division Property of Equality

Name: ______________________ ID: A

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37 What would you fill in the blank to complete the proof?

Given: SV Ä TU and "SVX # "UTXProve: VUTS is a parallelogram

Because "SVX # "UTX, 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 rhombusB 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 26

39 The vertices of "TVS are T(1,1), V(4,0), and S(3,5). Is the triangle scalene, isosceles, equilateral, or acute? A scalene C equilateralB isosceles D acute

Name: ______________________ ID: A

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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 centimetersG 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 = 73

D x = 21

Name: ______________________ ID: A

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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 If a point is not in the first quadrant, then

the coordinates of the point are not positive.H If the coordinates of a point are positive, then the point is in the first quadrant.J 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 If it has 4 legs, then it is a horse.

B Every horse has 4 legs.

C If it is a horse, then it has 4 legs.

D 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!1 ' 60°.

H If !1 is acute, then m!1 = 60°.

J If m!1 ' 60°, then !1 is not acute.

Name: ______________________ ID: A

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45 Which of the following must be true?The diagram is not to scale.

A AC < FH C AB < BCB BC < FH D AC = FH

46 If m!DBC = 92°, what is the relationship between AD and CD?

F AD < CD H AD = CDG AD > CD J not enough information

47 Find m!P. The diagram is not to scale.

A 50º B 60º C 40º D 130º

Name: ______________________ ID: A

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48 Which lines are parallel if m!3 = m!6? Justify your answer.

F r Ä s, by the Converse of the Same-Side Interior Angles TheoremG r Ä s, by the Converse of the Alternate Interior Angles TheoremH l Ä m , by the Converse of the Alternate Interior Angles TheoremJ 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 7.2G 6.2H 5.4J 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°?