Geometry Midterm Review

Name: ______________________ Class: _________________ Date: _________

ID: A

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

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How would you classify pairs of opposite angles in a parallelogram? complementary G supplementary F

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J

congruent adjacent

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

adjacent B complementary A

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H

supplementary D vertical C

What is the measure of an exterior angle of a regular twelve-sided polygon? 168° G 150° H 30° J 12° F

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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

Name: ______________________ 6

ID: A

What are the measures of the interior angles of the polygon shown?

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° F

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

m!A > 50; B m!A = 50; C m!A < 50; D m!A = 40; A

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Triangle-Angle Exterior Angle Exterior Angle Exterior Angle

Sum Theorem Theorem Theorem Theorem

Below is a regular octagon. What is the value of x ?

1440° G 1080° F

H J

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135° 90°

Name: ______________________ 9

ID: A

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

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B

QP # ST

C

PR # TR

D

QR # SR

PQR #

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?

148.5 yards G 146 yards H 141.5 yards J 123.5 yards F

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Name: ______________________ 11

ID: A

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?

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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.

Which of the following diagrams shows a parallelogram? F

G

H

J

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Name: ______________________ 13

Find the values of the variables in the parallelogram. The diagram is not to scale.

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

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C D

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

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

F G H J

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ID: A

x x x x

= = = =

24, y 30.5, 34, y 54, y

= 24 y = 11 = 18 = 44

Which parallelograms have congruent diagonals? A rhombuses or squares B rhombuses or rectangles C rectangles or kites D rectangles or squares

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Name: ______________________ 16

Quadrilateral LMNO is a rhombus.

What is m!PLM? F 160° G 120° 17

ID: A

H J

100° 60°

QRST it an isosceles trapezoid and m!R = 116. What are m!S, m!Q, and m!T?

m!S = 64, m!Q = 64, m!T = 116 B m!S = 116, m!Q = 64, m!T = 64 A

m!S = 64, m!Q = 64, m!T = 64 D m!S = 116, m!Q = 116, m!T = 116 C

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Name: ______________________ 18

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ID: A

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

G

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

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.

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 SAS B AAS D SSS

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Name: ______________________ 20

ID: A

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.

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Name: ______________________ 21

ID: A

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

Statements 1. JKLM is a parallelogram. 2. KL Ä JM 3. !J and !K are supplementary. 4. JK Ä ML 5. !L and !K are supplementary. 6. !J # !L

Reasons 1. Given 2. Definition of a parallelogram 3. ? 4. Definition of a parallelogram 5. (Same as step 3.) 6. !J and !L are supplements of the same angle.

Same-Side Interior Angles Theorem B Corresponding Angles Theorem C Same-Side Exterior Angles Theorem D Triangle Angle-Sum Theorem A

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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

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J

I, II, or II

Name: ______________________ 23

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ID: A

Which of the following is an illustration of a median?

A

C

B

D

In the figure, XW is the perpendicular bisector of YZ, ZY = 11g, and XY = 20g. which expression represents the length of XZ?

20g 11g H 10g J 5.5g F

G

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Name: ______________________ 25

ID: A

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

SSS B SAS

ASA D SSA

A

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If "MNO # "PQR, which of the following can you NOT conclude as being true? F

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C

MN # PR

G

H

!M # !P

NO # QR

J

!N # !Q

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; FD

B

yes, by AAS; ED

yes, by SAS; ED D No, the two triangles are NOT congruent. C

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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

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Name: ______________________ 29

ID: A

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

Statement 1. !Q # !T and

Reasons 1. Given

QR # TR 2. !PRQ # !SRT

2. Vertical angles are congruent.

3. "PRQ # "SRT

3.

?

4. PR # SR

4.

?

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

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AAS; Corresp. parts of # " are #. D ASA; Corresp. parts of # " are #. C

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

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Name: ______________________ 31

ID: A

Which angle has the greatest measure?

A

!1 B !2 C !3 D !4

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What is the smallest angle of "ABC?

Two angles are the same size and smaller than the third. G !B H !A J !C F

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Which three lengths could be the lengths of the sides of a triangle? A 12 centimeters, 5 centimeters, 17 C 9 centimeters, 22 centimeters, 11 centimeters centimeters B 10 centimeters, 15 centimeters, 24 D 21 centimeters, 7 centimeters, 6 centimeters centimeters

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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

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Name: ______________________ 35

ID: A

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 Property

Alternate Interior Angles Theorem Substitution Property C Vertical Angles Theorem D Given A B

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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

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Name: ______________________ 37

ID: A

What would you fill in the blank to complete the proof? Given: SV Ä TU and "SVX # "UTX Prove: 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 a quadrilateral is both congruent and parallel, then A rectangle C B square D

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39

is a __________ because if one pair of opposite sides of the quadrilateral is a parallelogram. rhombus parallelogram

What is the distance between the two points in simplest radical form? G(1, 3) and J(2, 8) F G 2 13 H 6 J 130

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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 equilateral B isosceles D acute

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Name: ______________________ 40

ID: A

Abigail knows that the figure below is a regular pentagon with a perimeter of 70 centimeters.

What is the value of x? 10 centimeters G 12 centimeters F

41

H J

14 centimeters 16 centimeters

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?

x=2 7 B x= 3 A

C

x = 15

D

x = 21

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Name: ______________________

ID: A

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.

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Write a conditional statement from the following statement: A horse has 4 legs.

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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.

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.

17

Name: ______________________ 45

ID: A

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

AC < FH B BC < FH

AB < BC D AC = FH

A

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C

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

AD < CD G AD > CD F

47

J

AD = CD not enough information

C

40º

H

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

A

50º

B

60º

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D

130º

Name: ______________________ 48

ID: A

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 Theorem

G

r Ä s, by the Converse of the Alternate Interior Angles Theorem

H

l Ä m, by the Converse of the Alternate Interior Angles Theorem

J

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? 7.2 G 6.2 H 5.4 J 4.8 F

Short Answer 51

What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 53°?

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