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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

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

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

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 andCAB 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

AM MB

Def of midpoint

AD BC

DM CM

M is the

midpoint of AB.

ABCD is an

isosceles trap.

given

given

Def isos.trap.

CPCTC

?

ΔADM ΔBCM

What is the missing statement and reason that completes the proof?

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

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

4) Angle Addition Postulate

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

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

quadrilateral

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

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

ABCD is a trapezoid with median EF. What is the length of AB?

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

What is the slope of the line that is perpendicular to the line whose equation is:

C

ABCD is a rhombus. The slope of AB is 3/8. What is the slope of DC?

B

Which of the following is an equation of the line perpendicular to:

D

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

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