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SEMESTER EXAM. REVIEW. S. T. U. V. Which of the following best describes what  SVT and TVU have in common?. A. A. B. C. O. F. D. E. Which of the following is a pair of supplementary angles?. D. A. F. B. N. J. C. G. M. K. H. D. E. I. S. Q. T. U.

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SEMESTER

EXAM

REVIEW

S

T

U

V

Which of the following

best describes what

 SVTand TVU have in common?

A

A

B

C

O

F

D

E

Which of the following is a pair of supplementary angles?

D

A

F

B

N

J

C

G

M

K

H

D

E

I

S

Q

T

U

Which two angles

C

Plane P contains points A, B, and C. A different plane, plane Q, contains points B, C, and D. Which of the following represents the intersection of P and Q?

B

What are the coordinates of the midpoint of

EF?

F(- 6, 10, 0)

E(3, 4, - 5)

B

(206, 196) in the xy-plane?

C

Mt. Lookout (78,71)

Using the map, the highway department locates two exits between Tomstown and Mount Lookout. From Tomstown, Exit 1 is halfway to Mount Lookout, and Exit 2 is three-fourths of the way to Mount Lookout. What are the coordinates for Exit 2?

Exit 2

Exit 1

Tomstown (2, 3)

B

In the xy-plane, (-3, 1) and (4, 3) are endpoints of a diameter of a circle. What are the coordinates of the center of the circle?

A

(12, 9)

(0,8)

(12, 3)

(0,2)

The county planning department designs a new park in the shape of a parallelogram. They put in two diagonal walkways.

What will be the coordinates of the intersection of the diagonal walkways?

D

Given: m1 = 4 x,

m 2 = (3 x + 10), and

m 3 = (2 x + 17). What is m  2?

A

A

B

1

C

D

If ABCD is a rhombus and

m  ABC = 80, what is the measure of

 1?

A

ABCD is a parallelogram. If

m BCD = (6 x – 20) and

m DAB = (2 x + 80), what is the value of x?

D

M

12 in.

25 in.

N

28 in.

O

Which of the following statements about the picture is true?

B

If two angles are not supplementary, then they form a linear pair.

If two angles form a linear pair, then they are supplementary.

If two angles do not form a linear pair, then they are supplementary.

Write the following statement in “If-then” form.

B

“Two angles that form a linear pair are supplementary.”

If the triangle is not scalene, then there are two congruent angles.

If two angles of a triangle are congruent, then the triangle is scalene.

If there are two congruent angles in a triangle, then the triangle is not scalene.

If the triangle is not scalene, then there are no congruent angles.

What is the inverse of the statement below?

If a triangle is scalene, then no two angles are congruent.

A

If the triangle does not have two congruent sides, then it is not isosceles.

If a triangle has two congruent sides, then it is isosceles.

If a triangle is isosceles, then it has two congruent sides.

A triangle has two congruent sides if and only if it is isosceles.

What is the contrapositive ofthe statement below?

If a triangle is isosceles, then it has two congruent sides.

A

A is an acute angle.

A is not an acute angle.

The complement of A is not an acute angle.

The supplement of A is not an acute angle.

The conditional statement “All 45° angles are acute angles” is true. Based on the conditional statement, which of the following can be concluded from the additional statement “The measure of  A is 45°”?

A

then alternate interior angles are congruent.

then vertical angles are congruent.

then alternate exterior angles are congruent.

then corresponding angles are congruent.

t

n

If k | | m | | n,

Which of the statements justifies the conclusion that 1  2  3?

3

m

2

k

1

D

A

D

C

B

It is given that AC  AD andCAB  DAB. By the reflexive property of congruent segments, AB  AB.

side-angle-side

hypotenuse-leg

side-side-side

angle-side-angle

Which reason could be used to prove

ΔABC  ΔABD?

A

A

M

B

C

D

Given: ABCD is an isosceles trapezoid. M is the midpoint of AB.

Prove: DM  CM

AM  MB

Def of midpoint

DM  CM

M is the

midpoint of AB.

ABCD is an

isosceles trap.

given

given

Def isos.trap.

CPCTC

?

AD  BC; the legs of an isosceles trapezoid are congruent.

MAD  MBC; the base angles of an isos. trap. are congruent

AM  BM; corresponding parts of congruent triangles are congruent

 ABC  DAB; if lines are parallel, s-s int.angles are supp.

B

X

Y

B

A

C

Given: Δ ABC

Prove: m  BAC + m  ABC + m  BCA

= 180

STATEMENTS

REASONS

• Exactly one parallel line can be
• drawn to given line from pt. not on
• line.
• Draw XY through B and parallel
• to AC.

2) XBA and ABY form a linear pair.

2) Definition of a linear pair

3) m  XBA + m ABY = 180

3) The sum of the measures of the

angles of a linear pair is 180.

4) m  ABC + m CBY = m  ABY

5) Substitution

5) m  XBA + m ABC + m  CBY

= 180

6) ____________________________

6) CBY  BCA and  XBA   BAC

7) Definition of congruent angles

7) m CBY = m BCA and

m  XBA = m  BAC

• Substitution
• m  BAC + m  ABC + m  BCA
• = 180
What is the reason for statement 6 in the proof?

Alternate interior angles of parallel lines are congruent.

Alternate exterior angles of parallel lines are congruent.

Vertical angles of parallel lines are congruent.

Corresponding angles of parallel lines are congruent.

A

40°

y

x

40

60

60°

100

80

What is the measure of angle y?

D

B

BD is the angle bisector of ABC. If m A = m  C = 50, what is m  ABD?

C

A

D

30

40

50

45

B

OB bisects  AOC. If m AOB = (3 x + 16) and m  BOC = (8 x – 14), what is m  AOB?

18

26

48

34

C

c

2

1

a

Line a is parallel to line b.

4

3

Line a is parallel to line c.

b

Line a is perpendicular to line c.

Line b is perpendicular to line c.

• 1 is supplementary to
• 3 under which of the following conditions?

A

triangle

hexagon

pentagon

For which type of convex polygon is the sum of the measures of the interior angles equal to the sum of the measures of the exterior angles, one at each vertex?

D

Q

R

S

120°

P

T

240

360

U

720

600

If m  P = 120º, what is the sum of the measures of the remaining interior angles?

C

4

5

8

9

The measure of each exterior angle of a regular polygon is 45. How many sides does the polygon have?

C

(2, 1)

(3, 2)

(4, 1)

(5, 1)

An isosceles triangle has vertices at (1,1) and (3, 3). Which of the following could be the coordinates of the third vertex?

D

isosceles

right

scalene

equilateral

Triangle MNO has vertices with coordinates M (0, 2),

N (1, 0), and O (5, 1). What type of triangle is ΔMNO?

C

In triangle XYZ, W is between Y and Z. The coordinates are X (2, 3),

Y (5, 0), Z (0, 0), and

W (2, 0). What is

XW?

altitude

angle bisector

median

perpendicular bisector of the side

A

parallelogram

rectangle

rhombus

trapezoid

What is the most specific name for quadrilateral ABCD with vertices A (0, 0), B (3, 4), C (6, 0), and

D (3, - 4)?

C

16

18

24

32

In rectangle ABCD, diagonal

AC = (3 x – 9) and diagonal

BD = (x + 13). What is AC?

C

20

16

10

8

In parallelogram RSTU, the diagonals intersect at E.

If RE = 10 and

SU = 16, what is RT?

A

C

B

A

3

2

1

an infinite number

If points A, B, C, and D form a trapezoid, how many ordered pairs could represent D?

D

A

B

x - 5

13

15

12

E

F

C

D

2x - 1

5 units

7 units

9 units

10 units

A

4 < x < 10

4 ≤ x ≤ 10

x > 4

x < 10

If the sides of a triangle are 3, 7, and x, which of the following best describes x?

A

C

Y

X

A

B

In ΔABC, X is the midpoint of AC and Y is the midpoint of BC. If m  C = 67 and

m  A = 72, what is m  CYX?

41

36

72

67

B

A triangle has interior angles that measure 3 x,

(2 x + 15), and (x + 45). What is the measure of the largest exterior angle?

B

In ΔABC, Z is the midpoint of AC and Y is the midpoint of BC. If YZ = 21 and

AB = (2 x – 4), what is x?

B

Y

C

Z

A

C

PQ is parallel to RS.

PQ is perpendicular to RS.

PR is perpendicular to QS.

PR is parallel to QS.

Given points P (7, 5),

Q (8, 3), R (0, - 1), and

(- 1, 1), which of the following is true?

A

B

P

k

Line k contains point P and the origin. Which is an equation of the line that is perpendicular to line k and passes through point P?

D