Geometry Level 1 Midterm Review Packet

I. Geometric Reasoning (Units 1 & 2) Circle the best answer. 1. If two planes intersect, then they intersect in exactly one ______.

A segment B line C point D ray

2. Which is an alternative name for LN ?

A L B NL C LK D LM

3. What is the distance between the points (6, 7) and (1, 5)?

A 13 B 53 C 13 D 119

4. W is the midpoint of VX . What is VX if VW 2x 5 and WX 4x 3?

A 4 B 13 C 8 D 26

5. Which is NOT a name for the angle at the right?

A P B QPR C PQR D RPQ

6. JK bisects LJM, which is an obtuse angle. What is the greatest possible whole-number

measure of LJK?

A 99 B 90 C 91 D 89

7. Which completes the sentence?

1 and 2 are _______ angles.

A adjacent

B complementary

C supplementary

D vertical

8. KLM and RST are complementary angles. mKLM (7x) and mRST (36 x).

What is the measure of the smaller angle?

A 9 B 30 C 27 D 63

9. What is the circumference to the nearest tenth of a millimeter, of a circle whose radius is

40 mm?

A 62.8 mm B 188.5 mm C 125.6 mm D 251.3 mm

10. What is the area of a square whose sides measure (x 8)?

A 2x 16 B x2 64 C 4x 32 D x2 16x 64

11. The midpoint of a segment is (9, 1). One endpoint of the segment is (2, 5). What are the

coordinates of the other endpoint of the segment?

A (16, 7) B (13, 9) C (20, 3) D (5, 6)

12. To the nearest tenth of a unit, what is the distance between (4, 5) and (8, 1)?

A 12.6 units B 7.2 units C 11.3 units D 4.5 units

13.Which transformation can you perform on the point (1, 10) to obtain (1, 10) as the image?

A reflection over the x-axis B reflection over the y-axis

C a rotation of 90 D a rotation of 180

14. What is the image of (6, 7) after a reflection over the y-axis?

A (6, 7) B (6, 7) C (6, 7) D (6, 7)

15. Which is a counterexample to the conjecture “All prime numbers are odd”?

A 0 B 3 C 2 D 4

16. Which is the hypothesis of the conditional statement “If a triangle is an obtuse triangle, then two

of its angles are acute.”

A If B a triangle is an obtuse triangle

C then D two of its angles are acute

17. Given: If an angle measures between 90 and 180, then the angle is obtuse.

mR 130. Which conjecture is valid?

A R is not acute. B R is not straight.

C R is not right. D R is obtuse.

18. Which is the contrapositive of the statement “If a line bisects a segment, then it divides the

segment into two congruent segments”?

A If a line divides a segment into two congruent segments, then it bisects the segment.

B If a line does not bisect a segment, then it does not divide the segment into two

congruent segments.

C If a line does not divide a segment into two congruent segments, then it does not bisect

the segment.

D If a line does not divide a segment into two congruent segments, then it bisects the

segment.

19. Given: If a child is at least 4 feet tall, then he or she can ride the roller coaster. If a child can

reach the red bar, then the child is at least 4 feet tall. Which conjecture is valid?

A If a child can reach the red bar, then the child can ride the roller coaster.

B If a child is at least 4 feet tall, then the child can reach the red bar.

C If a child can ride the roller coaster, then the child is at least 4 feet tall.

D If a child can ride the roller coaster, then the child can reach the red bar.

20. If k 8 0, what property justifies k 8?

A Distributive Property B Transitive Property of Equality

C Addition Property of Equality D Subtraction Property of Equality

21. Complete: By the Multiplication Property of Equality, if a b, then _______.

A ab ba B ac bd C ac bc D ab ab

22. Given: If a square has an area of 36 square units, then its perimeter is 24 units.

Which is a related biconditional statement for the given statement?

A If a square has a perimeter of 24 units, then it has an area of 36 square units.

B The perimeter of a square is 24 units if and only if it has an area of 36 square units.

C If a square does not have a perimeter of 24 units, then it does not have an area of 36

square units.

D If a square does not have an area of 36 square units, then it does not have a perimeter

of 24 units.

23. Which biconditional is false?

A A person is eligible to attend the club meetings if and only if that person is a member of

the club.

B A person can practice medicine in the United States if and only if that person has a

valid medical license.

C A person can legally drive a car if and only if the person holds a valid driver’s license.

D A student participates on the football team if and only if the student maintains at least a

B average.

24. Given: 1 and 2 are supplementary;

1 2

Prove: 1 is a right angle.

In a two-column proof, which is the statement in the final step?

A Right Angle Congruence Theorem

B 1 and 2 are supplementary.

C 1 is a right angle.

D Definition of right angle

25. Given: m1 (60 x), m3 x

Prove: m2 150

Proof: By the Vertical Angles Theorem, 1 3, so 60 x x. Then, 60 2x

by the Addition Property of Equality. By the Division Property of Equality, 30 x,

or x 30. Since m3 30 and 2 and 3 form a linear pair, 30 m3 _______.

By the Subtraction Property of Equality, m3 150.

What information completes the proof?

A 90 C m1

B 180 D m2

26. Two angles form a linear pair. One angle measures (10x 63)o. The other angle measures

(8x)o. What is the value of x?

A 8.5 B 31.5 C 13.5 D Cannot be determined

27. If 7

3 6

n , which justifies the statement n

7

2?

A Substitution B Reflexive Property of Equality

C Division Property of Equality D Multiplication Property of Equality

II. Parallel and Perpendicular Lines (Unit 3) Part I. Circle the best answer.

1. Which statement is NOT true?

A Parallel lines do not intersect.

B A segment has exactly two endpoints.

C Two planes that do not intersect are always skew.

D A ray has exactly one endpoint.

2. How many different rays can be named using three collinear points P, Q, and R?

A 1 B 3 C 2 D 4

3. The midpoint of XY is Z. If XY 3n and XZ n 15, what is YZ?

A 18 B 45 C 36 D 90

4. In the figure, what is RS?

A 5 B 56

C 32 D 70

5 . In degrees, what is m1?

A 76 B 108

C 104 D 156

6. The measures of two supplementary angles are (3x 10)o and (6x 100)o. In degrees,

what is the measure of the smaller angle?

A 0 B 20 C 10 D 2

263

7. What is the area of a rectangle whose sides measure 2g and (g 5)?

A 3g 5 B 6g 10 C 6g 5 D 2g2 10g

8. To the nearest whole number, what is the circumference of a circle whose radius is 12.5?

Use 3.14 for .

A 20 B 79 C 39 D 491

9. The midpoint of VW is P(4, 3). If the coordinates of W are (0, 15), what are the

coordinates of V?

A (8, 21) B (4, 33) C (8, 21) D (2, 6)

10. What is the distance from (8, 1) to (3, 11) on the coordinate plane?

A 13 units B 24 units C 13 units D 34 units

11. What are the coordinates of the image of K(8, 7) after the translation

(x, y) (x 10, y 2)?

A (18, 5) B (18, 5) C (2, 9) D (2, 9)

12. Which transformation maps T(6, 3) to T(6, 3)?

A 90o rotation B 180o rotation

C reflection over the x-axis D reflection over the y-axis

13. Which is a counterexample that disproves the conjecture “If the area of a rectangle is 36

square units, then the perimeter is less than 36 units”?

A a 6 by 6 rectangle B a 4 by 9 rectangle

C a 3 by 12 rectangle D a 2 by 18 rectangle

14. Which conditional statement is true?

A If it is raining outside, then the ground is wet.

B If a person lives in the United States, then the person lives in Chicago.

C If a number is divisible by 3, then the number is odd.

D If today is Saturday, then yesterday was Sunday.

15. What is the inverse of the statement “If the key fits, then the lock opens”?

A If the lock opens, then the key fits.

B If the key does not fit, then the lock does not open.

C If the lock does not open, then the key does not fit.

D If the key fits, then the lock does

not open.

16. Given: If Maria passes geometry, then she will graduate. Maria passes geometry.

What can you conclude?

A Maria will take geometry.

B If Maria does not graduate, then she is not taking geometry.

C If Maria does not take geometry, then she will graduate.

D Maria will graduate.

17. Given: If all four angles of a parallelogram are right angles, then the parallelogram is a

rectangle. If a parallelogram has at least one right angle, then all four angles are right.

Which of the following conjectures is valid?

A If a rectangle has four right angles, then the rectangle is a parallelogram.

B If a parallelogram has at least one right angle, then the parallelogram is a rectangle.

C If all four angles of a parallelogram are right angles, then at least one angle is a right

angle.

D If a parallelogram is a rectangle, then the parallelogram has at least one right angle.

18. Which is a biconditional statement for the given conditional?

If two coplanar lines do not intersect, then they are parallel.

A Two coplanar lines intersect if and only if they are not parallel.

B Two coplanar lines do not intersect if and only if they are parallel.

C Two coplanar lines are not parallel if and only if they intersect.

D Two coplanar lines intersect if and only if they are parallel.

19. Which biconditional statement is true?

A Peter lives in Cincinnati if and only if he lives in Ohio.

B A rectangle has sides 3 and 5 if and only if its area is 15.

C Two segments are congruent if and only if they have the same measure.

D Two angles measure 90o if and only if they are supplementary.

20. If 6k 9 20 and k r, why is 6r 9 20?

A Addition Property of Equality B Multiplication Property of Equality

C Symmetric Property of Equality D Substitution Property of Equality

21. Which property justifies the statement “If 2y n and n 3, then 2y 3”?

A Transitive Property of Equality

B Reflexive Property of Equality

C Symmetric Property of Equality

D Multiplication Property of Equality

Refer to the figure for Exercises 22 and 23.

22. Which pair of angles are corresponding angles?

A 1 and 2 B 1 and 4 C 1 and 3 D 1 and 6

23. Which completes the statement “Angles 6 and 7 are an example of ________ angles”?

A same-side interior B alternate interior

C alternate exterior D corresponding

24. If lines p and q are parallel, what is the value of x?

A 15 B 45

C 30 D 90

25. If j k, which could be one of the angle measures?

A 25o B 60o

C 37o D 84o

26. If x 7, which lines must be parallel?

A r s only B s t only

C r t only D r s t

27. Which angle must be congruent to 8 to prove that u v?

A 1 B 3

C 2 D 4

28. Which inequality must be true, given the information in the figure?

A x 3 B 2 x

C x 3 D x 3

29. In the figure, ABD CBD. What is the value of x?

A 6 B 30

C 24 D 48

30. What is the slope of the line whose equation is 2x 6y 0?

A 1

3 B

2

3 C

1

3 D 3

31. What is the slope of a line parallel to the graph of y 1 8(x 2)?

A 8 B 1

2 C 2 D

1

8

32. Which is an equation of the line in the graph?

A

24 ( 3)

3y x

B 2

3 ( 4)3

y x

C 2

4 ( 3)3

y x

D 2

3 ( 4)3

y x

33. The graph of y 3x 8 coincides with the graph of 6x ay 16. What is the value of a?

A 2 B 1 C 1 D 2

Part II. Answer each below.

1. Identify a pair of skew segments.

________________________________________

2. Write True or False. Perpendicular lines cannot be skew lines.

________________________________________

3. How many total pairs of both alternate exterior and alternate interior angles are formed by a

transversal that intersects two coplanar lines at two different points?

________________________________________

Use the figure below to answer questions 4 and 5

4. Given: 8 and 6 are corresponding angles. Identify the transversal.

________________________________________

5. If is an alternate exterior angle, name two other angles that are alternate exterior angles

with it.

__________________________________

6. If parallel lines are intersected by a transversal that is not perpendicular to them, how many

pairs of nonadjacent supplementary angles are formed?

________________________________________

7. What one word completes the following sentence? ________ angles formed by a

transversal of parallel lines are congruent and all the ________ angles are supplementary

to all the obtuse angles.

________________________________________

8. Find the measure of QRS and state the postulate or theorem that justifies your answer.

________________________________________

________________________________________

9. If 1 6 and m1 90o, is r s?

________________________________________

10.Which values for x and y make lines

r, s, and t parallel?

________________________________________

11. If two parallel lines and a transversal form angles that are all congruent, describe the

relationship between the transversal and each of the parallel lines.

________________________________________

________________________________________

12. Write and solve an inequality for x.

________________________________________

13. If the slope of a line is 0, which type of line is it and what is true about the y-coordinates of

all points on the line?

________________________________________

14. If line r through (1, 1) and (5, 7) is parallel to line s through (4, 2) and

(x, y), what are possible values for x and y?

________________________________________

15. Write True or False. All horizontal lines are perpendicular to all vertical lines, so the product

of the slope of a horizontal line and the slope of a vertical line is 1.

________________________________________

16. Write True or False. Multiplying both sides of the equation for a line by the same nonzero

number will produce an equation for a line that coincides with the original line.

________________________________________

17. Write the equation of the line that passes through (4, – 3) and is parallel to y 2x + 7.

________________________________________

18. Write an equation in slope-intercept form for the line that passes through (6, 10) and is

perpendicular to 2x 3y 6.

III. Triangle Congruence (Unit 4) Part I. Circle the best answer.

1. Describe the transformation M: (x, y) (-y, x).

A A reflection across the y-axis.

B A reflection across the x-axis.

C A rotation 90o clockwise with center of rotation (0, 0).

D A rotation 90o counterclockwise with center of rotation (0, 0).

2. Which best describes ABC with vertices A(2, 1), B(0, 4), and C(2, 1)?

A acute B obtuse C equiangular D right

3. Which is a correct classification of DEF with vertices D(3, 2), E(2, 3), and F(1, 0)?

A equilateral B scalene C isosceles D Not here

4. What is the value of x?

A 41 B 99

C 58 D 122

5. QRS STQ, QS x2 10 and SQ 2x 2. What is the value of x?

A 4 B 2 C 2 D 4

6. ABC DEF. What information is NOT needed to find the perimeter of ABC if you are

given all four lengths below?

A DE B CF

C BG D EF

7. Given: ABC with vertices A(5, 2), B(5, 7), and C(1, 2). Which set of coordinates best

repositions the triangle to make a coordinate proof easier?

A (0, 0), (4, 0), and (4, 5) B (0, 0), (4, 0), and (0, 5)

C (0, 0), (0, 4), and (5, 0) D (0, 0), (4, 0), and (0, 5)

Use the figure for Exercises 8–11.

8. Given that AB y 3, DC 3y 1, EB 3y 1, ED y 1, AE y, and CE 2y.

What value of y proves AEB CED by the SSS Postulate?

A 2 B 1 C 1 D 2

9. What information would allow you to prove AED CEB by SAS?

A E is the midpoint of DB . B E is the midpoint of AC .

C E bisects AC . D E bisects both DB and AC .

10. If ADC and ABC are right angles, AC BD, and AB DC, which postulate or theorem

proves ABC CDA?

A SSS B ASA C SAS D HL

11. If AD BC and ABD CDB, which postulate or theorem could be used to prove

ABD CDB?

A SAS B SSS C ASA D HL

12. If the height of a right triangle is n units and the base is m units, which statement is NOT

true?

A The midpoint of the hypotenuse is (m, n).

B A(0, 0), B(m, 0), and C(0, n) can represent the vertices.

C The midpoint of the hypotenuse is , .2 2

m n

D The slope of the hypotenuse is

n

m .

13. What is mDAC?

A 30 B 60

C 45 D Not here

Use the partially completed two-column proof for Exercises 14 and 15.

Given: JK LK ; JYL and LXJ are rt. s .

Prove: JY LX

Proof:

Statements Reasons

1. KJL KLJ 1. ?

2. JL LJ 2. ?

3. JYL and LXJ

are rt. s .

3. Given

4. JYL LXJ 4. ?

5. JYL LXJ 5. ?

6. JY LX 6. ?

14.Which justification belongs in Step 1?

A Base Angles Theorem. B Reflex. Prop. of

C Right Theorem. D CPCTC

15. Which justification belongs in Step 5?

A ASA B AAS C HL D SSA

Part II. Answer each below

1. Prove that triangles F(4, 6), G(5, 7),H(7, 4) and J(1, -4), K(2, -5), L(4, -2) are congruent.

Use the figure for Exercises 2 and 3.

2. Classify ABC by angle measures. ___________________________________

3. Classify ABD by side lengths. __________________________________

Use the figure for Exercises 4 and 5.

4. What is mT ?

________________________________________

5. What is the value of y?

________________________________________

6. Given QRS STQ, R 4x2 4, and T 3x2 3x. What is mR?

________________________________________

7. Given QRS STQ, RS 3x 3, TQ 2x 2, and QR x2 2. What is the length of

side ?ST

________________________________________

Use the figure for Exercises 8–11.

8. If AD BC , write a statement about point E that

would allow you to prove AED CEB by the SSS Postulate.

________________________________________

9. Suppose AE CE and DEBE . What postulate or theorem will allow you to prove that

BEA DEC?

________________________________________

10. Write True or False. If ABC and DCB are right angles and ,AD BC you can prove

ABC DCB. _____________________________

11. DAB and BCD are right angles. Write a single congruence statement about two

segments that would allow you to conclude that DAB BCD. What theorem or

postulate would justify the conclusion?

______________________________________

12. What is the value of x?

________________________________________

IV. Properties and Attributes of Triangles (Unit 5)

Part I. Circle the best answer.

1. AC is the perpendicular bisector of .BD What is the value of x?

A 2.4 B 2

63

C 4 D Not here

2. In the figure at the right, what is mXYZ?

A 70o B 145o

C 125o D Not here

3. Which is the radius of a circle inscribed in KLM?

A the distance from the incenter to a side of the triangle

B the distance from the circumcenter to a side of the triangle

C the distance from the incenter to a vertex of the triangle

D the distance from the circumcenter to a vertex of the triangle

4. If (2, 4) is the location of the centroid of a triangle, which CANNOT be the coordinates of the

vertices of the triangle?

A (0, 0), (0, 6), (6, 6)

B (3, 4), (3, 2), (0, 6)

C (3, 2), (1, 6), (2, 8)

D (2, 0), (1, 8), (3, 4)

5. Which are the coordinates of the vertices of a triangle with orthocenter (4, 3)?

A (4, 1), (2, 5), (6, 5)

B (1, 0), (1, 5), (5, 3)

C (2, 0), (2, 5), (5, 3)

D (4, 0), (1, 5), (5, 5)

6. ABC is the midsegment triangle of TUV. Which measure CANNOT be determined?

A mVAC B mCBT

C mTAC D mAVC

7. PQ is the midsegment of GHK, and GH is the midsegment of KLM. What

is the length of PK ?

A 4 B 14

C 7 D 28

8. The length of a leg of a right triangle is two times the length of the other, and the

hypotenuse is 25. What is the length of the longer leg?

A 2 5 B 5 C 10 5 D 25

9. What is the value of x?

A 5 2

B 2 5

C 25 5

D 25 3

Part II. Answer each below.

1. In ABC, B is on the perpendicular bisector of AC , mA (6x 14)o,

and mABC (10x 2)o. Find mC.

________________________________________

2. Write an equation in point-slope form for the perpendicular bisector of the segment with

endpoints (2, 4) and (6, 2).

________________________________________

3. Find mDEF.

________________________________________

4. Find the center of the circle circumscribed about the triangle with vertices (0, 0), (8, 0), and

(6, 4).

________________________________________

5. TG and GV are angle bisectors of TUV. Find mVGT and the distance from G to .UV

________________________________________

________________________________________

6. Find the coordinates of the centroid of the triangle with vertices at (4, 2), (1, 2), and (6, 3).

________________________________________

7. Find the value of x.

________________________________________

8. What is mTAC?

________________________________________

9. List the angles of KLM with vertices K(2, 2), L(2, 6), M(7, 2) in order from smallest to

largest.

________________________________________

________________________________________

10. Determine the side lengths of the triangle.

________________________________________

11. Write True or False. Multiplying each number of a Pythagorean triple by a nonzero whole

number yields another Pythagorean triple.

________________________________________

12. Determine the perimeter of a square with a diagonal of 72 centimeters.

________________________________________