Download Unit 3: Geometry

Unit 3: Geometry
Name: ______________________
Quiz (Lessons 1 to 4)
Date: ________________
1. Identify the object as a line, ray, or line segment. Name the object.
a)
b)
D
B
c)
E
C
A
F
______________________
______________________
2. a) Name and measure the angles marked with arcs.
______________________
M
N
i) __________ = _______
ii) __________ = _______
Bonus► Name the quadrilateral in three ways.
______________________________
G
H
3. Mark the parallel sides and the right angles. Then identify the type of quadrilateral.
a)
b)
______________________
c)
______________________
______________________
4. a) Use a protractor and the given line segment to draw ABC = 42.
COPYRIGHT © 2015 JUMP MATH: TO BE COPIED. CC
b) Draw a line perpendicular to AB through point A.
B
A
Sample Unit Quizzes and Tests for AP Book 8.1
K-35
Unit 3: Geometry
Answer Key
Quiz (Lessons 1 to 4)
1.
a)
line segment AD or
line segment DA
2.
b)
line BE or line EB
c)
ray FC
a)
i)
GMN = 112º
ii) NHM = 62º
Bonus
Answers will vary.
Sample answer:
MNHG, MGHN,
NMGH
3.
a)
rectangle
b)
trapezoid
c)
parallelogram
Teacher to check.
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4.
K-36
Sample Unit Quizzes and Tests for AP Book 8.1
Unit 3: Geometry
Name: ______________________
Quiz (Lessons 5 to 8)
Date: ________________
1. Find the measure of the missing angle.
A
a)
H
b)
B
58º
D
23º
35º
O
C
______________________________
_____________________________
______________________________
_____________________________
______________________________
_____________________________
2. One angle of an isosceles triangle is 36. Find the measures of the other angles.
Hint: Make sketches to show the different options for placing the 36 angle.
3. Write “true” or “false.” If the statement is false, give a counterexample.
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a) The opposite angles in any
parallelogram are equal.
b) All scalene triangles are right triangles.
Bonus► Triangle MNO has M = 90, and N = 45. Classify the triangle.
Sample Unit Quizzes and Tests for AP Book 8.1
K-37
Unit 3: Geometry
Answer Key
Quiz (Lessons 5 to 8)
1.
a)
B = 180º − (90º
+ 58º)
= 180º − 148º
= 32º
b)
H = 180º − (23º
+ 35º)
= 180º − 58º
= 122º
2.
A triangle with angles 36º,
36º, and 108º.
A triangle with angles 36º,
72º, and 72º
3.
a)
true
b)
false
Counterexamples
may vary. Teacher to
check.
Bonus
O = 180º − 90º − 45º
= 45º
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MNO is a right isosceles
triangle.
K-38
Sample Unit Quizzes and Tests for AP Book 8.1
Unit 3: Geometry
Name: ______________________
Test (Lessons 1 to 8)
Date: ________________
1. Match the diagram to the correct description.
A.
B.
C.
a) The rays intersect. ______
b) If the rays are extended far enough, they intersect. ______
c) The rays do not intersect, even if they are extended. ______
2. a) Draw lines perpendicular to CD through points M and N. Label the intersection points.
M
N
D
C
b) Draw line segment MN. Name the quadrilateral you created. ______________________
c) Classify the quadrilateral. __________________________________
3. Measure the sides and the angles in the polygon. Mark the equal sides and
equal angles. Then classify the polygon. Be as specific as you can.
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a)
b)
___________________________
Sample Unit Quizzes and Tests for AP Book 8.1
_____________________________
K-39
Unit 3: Geometry
continued
Test (Lessons 1 to 8)
4. Find the measure of the missing angle.
a)
A
23º
B
b)
P
28
R
C
Q
5. One side of an isosceles triangle is 5 cm. The perimeter of the triangle is 13 cm.
What are the lengths of the sides of the triangle? Make sketches to show the
different options for placing the side that is 5 cm long.
6. If the statement is true, explain why. If the statement is false, give a counterexample.
a) If a triangle is equilateral, its angles are all equal to 60.
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b) A trapezoid cannot have two equal opposite sides.
Bonus► Can a triangle have two right angles? Explain.
K-40
Sample Unit Quizzes and Tests for AP Book 8.1
Unit 3: Geometry
Answer Key
Test (Lessons 1 to 8)
1.
2.
a)
A
b)
C
b)
c)
B
a)
Teacher to check.
b)
Sample answer:
CMND
c)
trapezoid or
Sample
counterexample:
right trapezoid
3.
a)
false
29 mm
29 mm 137º 43º
43º 137º 29 mm
29 mm
Bonus
No. The angles in a triangle
add to 180º. If two of the
angles are right angles,
then 90º + 90º = 180º, so
the third angle measures
zero. This doesn’t make a
triangle.
rhombus
b)
26 mm
95º
4 cm
32º
53º
5 cm
scalene obtuse
triangle
4.
a)
A = 180º − (28º
+ 90º)
= 180º − 118º
= 67º
b)
R + Q = 180º − 28º
= 152º
R = Q = 152º ÷ 2
= 76º
5.
5 cm
5 cm
3 cm
4 cm
4 cm
5 cm
6.
a)
true
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Sample answer:
The angles in an
equilateral triangle
are all equal. The
sum of the angles in
a triangle is 180º, so
each angle equals
180º ÷ 3 = 60º.
Sample Unit Quizzes and Tests for AP Book 8.1
K-41
Unit 3: Geometry
Name: ______________________
Quiz (Lessons 9 to 12)
Date: ________________
B
1. The triangles shown are congruent. Identify the equal sides
and equal angles. Then write the congruence statement.
__________ = __________, __________ = __________,
__________ = __________, __________ = __________,
A
D
F
__________ = __________, __________ = __________
Congruence statement: __________________________
C
E
2. a) What is the measure of DBC? _____
How do you know?
A
4.9 cm
3 cm
70 B
E
5 cm
C
5 cm
b) Write the pairs of equal sides and equal angles
in triangles AEB and BCD.
3 cm
75
__________ = __________
D
__________ = __________
__________ = __________
Triangles AEB and BCD are congruent by the _______ congruence rule.
c) DC = _____ = _____ cm
d) Which angle in AEB equals BDC? _______
What is the measure of these angles? _______
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Bonus► What is the measure of the third pair of angles in triangles AEB and BCD? Explain.
K-42
Sample Unit Quizzes and Tests for AP Book 8.1
Unit 3: Geometry
Answer Key
Quiz (Lessons 9 to 12)
1.
AB = FE
BD = EC
AD = FC
A = F
B = E
D = C
△ABD ≅ △FEC
2.
a)
70º
DBC and ABE
are vertical angles,
so they are equal.
b)
BE = CE
AB = DB
ABE = DBC
SAS
c)
AE, 4.9
d)
EAB
75º
Bonus
Angles in a triangle
add to 180º, so
E = 180º − (A
+ EAB)
= 180º − (75º
+ 70º)
= 35º
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△AEB ≅ △DCB,
so E = C,
so C = 35º
Sample Unit Quizzes and Tests for AP Book 8.1
K-43
Unit 3: Geometry
Name: ______________________
Quiz (Lessons 13 to 16)
Date: ________________
1. Find the missing angle. Show your work
a)
b)
76
29
x
x
x = ______
x = ______
2. Find the missing alternate, corresponding, supplementary, or vertical angles.
a)
b)
46
61
y
x
y
x = ______, y = ______
x = _______, y = ______
3. Lines ℓ and m are parallel. Use what you know about
corresponding and supplementary angles to explain
why x + y = 180°.
ℓ
x
m
y
z
A
Bonus► Zara says that AE is parallel to CD.
Is she correct? Explain.
1.5 in
2 in
B
E
C
2 in
1.5 in
D
K-44
Sample Unit Quizzes and Tests for AP Book 8.1
COPYRIGHT © 2015 JUMP MATH: TO BE COPIED. CC
x
Unit 3: Geometry
Answer Key
Quiz (Lessons 13 to 16)
1.
a)
x = 90º + 29º
= 119º
b)
x = 76º ÷ 2
a)
x = 61º
= 38º
2.
y = 119º
b)
x = 46º
y = 134º
3.
z and x are
corresponding angles, so
z = x.
y and z are
supplementary angles, so
y + z = 180º.
y + x = y + z = 180º
Bonus
Yes. ABE = DBC since
they are vertical angles.
AB = BD and EB = CB
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By the SAS rule,
△ABE ≅ △DBC, so
EAB = CDB. These are
alternate angles at lines AE
and CD. When alternate
angles are equal, lines are
parallel, so AE ∥ CD.
Sample Unit Quizzes and Tests for AP Book 8.1
K-45
Unit 3: Geometry
Name: ______________________
Test (Lessons 9 to 16)
Date: ________________
1. Use the congruence statement ABC  XYZ  PQR and A = 50, Y = 60
to find the measures of all angles in all three triangles.
2. Identify the congruence rule that tells you that the pair of triangles is congruent.
a)
b)
Congruence rule: _______
c)
Congruence rule: _______
Congruence rule: _______
3. Fill in all the missing angles. Mark parallel lines if they are not marked already.
a)
b)
c)
69
55
69
113
53
58
135
4. Use congruent triangles to explain why MON is isosceles.
O
M
K-46
L
N
Sample Unit Quizzes and Tests for AP Book 8.1
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69
Unit 3: Geometry
continued
Test (Lessons 9 to 16)
5. Are the quadrilaterals congruent? Use a ruler and a protractor to check.
If yes, write the pairs of corresponding equal sides and corresponding
equal angles. Then write the congruence statement.
W
B
C
U
A
D
V
X
Bonus► Use the grid to draw a counterexample to this statement:
If triangles ABC and DEF have AB = DE, BC = EF,
and A = D, they are congruent.
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Hint: Sketch the triangles first.
Sample Unit Quizzes and Tests for AP Book 8.1
K-47
Unit 3: Geometry
Answer Key
Test (Lessons 9 to 16)
1.
A = X = P = 50º
B = Y = Q = 60º
C = Z = R = 180º −
(50º + 60º)
Bonus
Answers may vary.
Teacher to check.
Sample answer:
= 180º − 110º
= 70º
2.
3.
a)
ASA
b)
SAS
c)
SSS
a)
111 69
69 111
67
113
111
69
b)
B
A
C
E
69
111
125
55 125
55 125 55
D
F
135 45
45
c)
111
69
58
69
53
58
122
4.
ML = NL
LO = OL
MLO = NLO = 90º
By the SAS rule,
△MOL ≅ △NOL,
so MO = NO and
△MON is isosceles.
AB = WU
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5.
BC = UX
CD = XV
AD = WV
A = W
B = U
C = X
D = V
ABCD ≅ WUXV
K-48
Sample Unit Quizzes and Tests for AP Book 8.1