Geometry
Unit 2 – Practice Test A
Name__Solutions__
Date___________________
Hour___________________
Objective 3 – Proofs involving angles: G.CO.9
For #1-2, solve for the given angle and then state which Theorem or
Definition allowed you to find the measure of the angle and why.
4/4 A
3/4 B
NY
7
8
If m ∠ 8 = 73 ° , then
6
5
1. m ∠ 7 = __107˚__
Theorem or Definition & why: __ ∠ 8 and
∠ 7 are a linear pair and because of the Linear Pair Theorem
they add up to 180˚; 180 – 73 = 107
2. m ∠ 5 = __73˚____
Theorem or Definition & why: __ ∠ 8 and
∠ 5 are vertical angles; vertical angles are equal because of the
Vertical angle Theorem
For #3-4, complete the proof using a two column proof or a paragraph proof. Either way, you must support
every step of your reasoning with Theorems, Definitions, or Properties
3. Given: ∠1 ≅ ∠A
1
A
Prove: ∠2 ≅ ∠A
2
(I first mark my picture for the given congruent angles. See red above.)
1 and
1 and
A are congruent because that information is given to me. I also know that
2 are congruent because they are vertical angles and the Vertical angle
Theorem says they are equal. So, by the transitive property of congruence
congruent to
4. Given:
2 will be
A.
(I first mark my picture for the given congruent angles. See below.)
Prove:
Given
1.
4 ≅
Statement
2
1. Given
2.
2 +
3 = 180
2. Definition of a linear pair.
3.
4 +
3 = 180
3. Substitution of
4.
4 ≅
5.
1 +
1
3 = 180
4 for
2.
4. Vertical Angle Theorem
5. Substitution of
1 for
4.
Unit 2 – Practice Test A
Objective 2: Constructions G.CO.12
5. Construct the perpendicular bisector of the segment.
Directions:
1. Put compass on one endpoint,
go over halfway & make an arc
2. Keep the compass setting the same,
repeat from the other endpoint.
3. Make a line between the 2 places
where the arcs overlap.
7.
Accurately draw two congruent segments.
Label the length of each segment.
Choice 1: Draw a segment, measure it and
draw another the same length.
Choice 2: Draw a segment, measure it with
your compass, draw another line and mark
off the compass measurement.
6.
Construct
4/4 A
3/4 B
NY
the bisector of
Directions:
Put compass on vertex,
make an arc that crosses both rays.
2. From each crossing point (P and Q),
make arcs in the middle that cross.
3. Draw a line from the vertex
to the crossing point.
8. Accurately draw two congruent angles
Label the measure of each angle.
1. Draw an angle.
2. Draw a line to start the second angle.
3. Draw an arc from the vertex of each angle
crossing both rays.
4. Measure from point B to point C with the
compass. Use the same measurement for new angle.
5. Complete the angle by drawing the ray.
Objective 4: Midpoint and Distance Formula in the Coordinate Plane G.GPE.4, G.GPE.7
9.
Find the coordinates of the midpoint of the segment
whose endpoints are H(8, 2) and K(6, 10).
To get the x point: (8 + 6)
To get the y point: (2 + 10)
2
2
x = 7
y = 6
9. ___(7, 6)
is the midpoint
10.
Find the distance between points
10. ___7.8 units____
P(8, 2) and Q(3, 8) to the nearest tenth.
Distance Formula Option
See last page for Pythagorean Theorem Option
2
2
D = √(3 - 8) + (8 – 2)
D = 7.8
11.
The Frostburg-Truth bus travels from Frostburg Mall through the City Center to Sojourner Truth
Park. The mall is 3 miles west and 2 miles south of the City Center. Truth Park is 4 miles east and 5 miles
north of the Center. How far is it from Truth Park to the Mall to the nearest tenth of a mile?
The mall is at (-3, -2). Truth Park is at (4, 5).
11. _10 miles__
Distance Formula Option
D = √(4 - -2)2 + (5 – -3)2
D = 10
See last page for Pythagorean Theorem Option
12.
A high school soccer team is going to Columbus to see a professional soccer game. A coordinate grid is
superimposed on a highway map of Ohio. The high school is at point (3, 4) and the stadium in Columbus is at
point (7, 1). The map shows a highway rest stop halfway between the cities. What are the coordinates of the
rest stop?
Halfway is the midpoint.
12. __(5, 2.5)_____
To get the x point: (3 + 7)
To get the y point: (4 + 1)
2
2
x = 5
y = 2.5
Unit 2 – Practice Test A
Objective 4 – Distributed Practice
4/4 A
3/4 B
NY
=
, and m
=
. X = 47.
13. m
Are
and
Complementary, Supplementary, or Vertical angles?
Give evidence to support your reasoning.
13. I will take each angle and substitute in 47 for x.
DFG = x + 5
JKL = x – 9
Conclusion: The angles are not vertical
DFG = 47 + 5
JKL = 47 – 9
because they are not equal. If I add 52
DFG = 52˚
JKL = 38˚
52 + 83 = 90, that means the angles
are complementary.
, and x = 10.
and
14.
Prove whether or not
bisects
.
Give evidence to support your reasoning. The diagram is not to scale.
14. I will take each angle and substitute in 10 for x. I know that a bisector cuts an angle in half
and gives me two equal parts so I am looking to see if the two angles are equal because that would
mean they are bisected.
LMO = 8x - 23
NMO = 2x + 37
Conclusion: Yes, MO does biscet
LMO = 8(10) – 23
NMO = 2(10) + 37
because the two angles are equal.
LMO = 57˚
NMO = 57˚
15. On a number line, point A is at -2 and point B is at 4. What is the location of point C between A and B, such
that AC is 2/3 the length of segment AB? Give evidence to support your reasoning by writing out your work
and drawing a number line.
B
A
C
15. First, I want to find the length of AB.
AB = -2 – 4
OR
AB = 6
Second, I need to find 2/3 of AB which is 6. So, I multiply: 2/3 x 6 = 4
AB = 2 + 4
AB = 6
OR
0.66 x 6 = 4
I now know that AC must be 4 units from A. So, point C must be at 2.
16. Given the number line below, what is the ratio of DE to EF? Point D is at -6, point E is at -2, and point F is
at 4.
D
E
F
16. ____________________
First, a ratio can be written as a fraction or with :
DE
Second, I need to find the length of each section.
EF
DE = -6 - -2
EF = -2 – 4
DE = 4
EF = 6
Now to write the ratio 4 = 2
6
3
OR
DE:EF
OR
4:6 simpified 2:3
How to use the Pythagorean Theorem instead of the distance formula.
10.
Find the distance between points
P(8, 2) and Q(3, 8) to the nearest tenth.
a. Plot the points on a graph and make a right triangle.
b. Count the length of each leg of the right triangle.
6 and 5 for this triangle
c. Plug the numbers in the Pythagorean Theorem formula
to get C (the hypotenuse)
a2 + b2 = c2
62 + 52 = c2
√61 = c2
7.8 = c2
C
6
5
The points are 7.8 units apart.
11.
The Frostburg-Truth bus travels from Frostburg Mall through the City Center to Sojourner Truth
Park. The mall is 3 miles west and 2 miles south of the City Center. Truth Park is 4 miles east and 5 miles
north of the Center. How far is it from Truth Park to the Mall to the nearest tenth of a mile?
The mall is at (-3, -2). Truth Park is at (4, 5).
a. Plot the points on a graph and make a right triangle.
b. Count the length of each leg of the right triangle.
7 and 7 for this triangle
c. Plug the numbers in the Pythagorean Theorem formula
to get C (the hypotenuse)
a2 + b2 = c2
72 + 72 = c2
√98 = c2
9.9 = c2
Truth Park and the Mall are 9.9 miles apart.
C
7
7