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Score_____=______ Notes _____________
10
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7th Grade Accelerated Chapter 9 & 10 Review
1. Points E, F, G, and H are all in plane S. Can
and
be skew?__________Explain your reasoning.
______________________________________________________________________________
2. The measure of
is 88 Ray BD bisects
. What are the measures of
and
? ______ Are
these two angles congruent? ____________Explain._________________________________________
_________________________________________________________________________________
3.
3. Line segment XY has a length of 16 units. Point Z is the midpoint of
. Point V is the midpoint of
the length of
? _____________What line segment is congruent to
?________________
. What is
4. Write the order of the side lengths from largest to smallest.
_____, ______, ______
5. Triangle HIJ is congruent to
. The measure of
is 32, the measure of
is 62, and the measure of
is 86. What are
,
, and
? ___________Explain your reasoning._______
________________________________________________________________________________________
__
6. A circle with center E and line segments have been drawn. The lengths of
,
, and
are all different from
each other. Is it possible for points F, G, and H to be on the same arc of the circle with center E?
_________Explain.________________________________________________________________________
7. Kevin constructed a triangle that is congruent to
. To make sure the new triangle is congruent to
he used
,
, and the included side. Name the side that Kevin used to construct the new triangle.
,
________________
8. The measure of
is 64. Ray RT bisects
. What are the measures of
and
?_______ Are
these two angles congruent?___________ Explain.__________________________________________
__________________________________________________________________________________________
9. The measure of
is 23. What is the measure of an angle supplementary to
the measure of an angle complementary to
?___________________________
10. The figure shown includes pairs of supplementary angles and pairs of vertical angles.
? __________What is
a.
The measure of
is 85. What are
, __________
,___________ and
?____________
Explain your reasoning.____________________________________________________________________
b.
The measure of
linear pair.
is 80. Name a linear pair that includes
. Write the measure of each angle in the
11.
88 mm, 97 mm, 92 mm. Determine whether it is possible to form a triangle using the set of
segments with the given measurements. Explain your reasoning. __________________________________
______________________________________________________________________________________
Multiple Choice
____ 12. The measure of
a.
b.
c.
d.
is 68. What is the measure of its supplementary angle?
22
90
112
180
____ 13. Terry measured an angle with a protractor. She aligned one side with the bottom of the protractor. The other side
passes through the mark that reads 110 and 70. The angle is acute. What is the measure of the angle?
a.
b.
c.
d.
40
70
110
180
____ 14. Which of the following has zero width and an infinite length?
a.
b.
c.
d.
a point
a line segment
a line
a plane
____ 15. A ray bisects an obtuse angle into two congruent angles. What type of angles are these two congruent angles?
a.
b.
c.
d.
acute
right
obtuse
straight
____ 16. Ray EF contains points G and H. What is the endpoint of
a.
b.
c.
d.
E
F
G
H
?
____ 17. The midpoint of
a.
b.
c.
d.
is Y. The length of
is 4 centimeters. What is the length of
?
4 cm
6 cm
8 cm
10 cm
____ 18. John measures an angle with a protractor. He aligned one side with the bottom of the protractor. The other side
passes through the mark that reads 135 and 45. The angle is obtuse. What is the measure of the angle?
a.
b.
c.
d.
45
90
135
180
____ 19. Line segment AB has a length of 24 units. Point C is the midpoint of
the length of
?
a.
b.
c.
d.
is 57. What is the measure of its complementary angle?
33
90
123
180
____ 21. Angle A is congruent to
a.
b.
c.
d.
. What is
6 units
12 units
24 units
48 units
____ 20. The measure of
a.
b.
c.
d.
Point D is the midpoint of
. Angle A measures 60. What is the measure of
?
30
60
120
180
____ 22. What is the first step to duplicate a given line segment AB?
a.
b.
c.
d.
Label point C on
Draw a starter line.
Set your compass at length
Place the compass at C.
.
____ 23. The lengths of two sides of a triangle are 3 cm and 7 cm. What can you conclude about the maximum length of
the third side of the triangle?
a.
b.
c.
d.
The maximum length of the third side must equal 10 cm.
The maximum length of the third side must be greater than 10 cm.
The maximum length of the third side must be less than 10 cm.
The maximum length of the third side must equal 4 cm.
____ 24. A triangle has angle measures 23 and 35. What is the measure of the third angle?
a. 32
b. 90
c. 122
d. 180
____ 25. Figure GHIJ is congruent to figure NOPQ. What pair of angles must be congruent?
a.
b.
c.
d.
and
and
and
and
____ 26. What is the measure of
a.
b.
c.
d.
?
30
63
147
150
____ 27. The lengths of two sides of a triangle measure 8 feet and 14 feet. What is the largest whole number value that the
third side could measure?
a.
b.
c.
d.
21 feet
22 feet
23 feet
24 feet
____ 28. You can construct congruent triangles if you know which of the following?
a.
b.
c.
d.
the measures of three sides
the measures of two angles and one given side
the measures of two sides and the included angle
all of the above
____ 29. A triangular bike path is exactly 9 miles long. If each of the three connecting paths is a whole-number of miles
long, which could be the lengths of the paths?
a.
b.
c.
d.
1 mile, 1 mile, 7 miles
1 mile, 2 miles, 6 miles
2 miles, 2 miles, 5 miles
2 miles, 3 miles, 4 miles
____ 30. In the two triangles shown,
.
Which congruency statement describes the relationship between the two triangles?
a.
b.
c.
d.
____ 31. What can you conclude about ACD using the Exterior Angle Inequality Theorem?
a.
b.
c.
d.
the measure of
the measure of
the measure of
the measure of
ACD is less than 121
ACD is greater than 121
ACD is less than the sum of 121 and 17
ACD is greater than the sum of 121 and 17
End of Chapter Test
Solve for x.
32.
___________________
33. Philippe cuts the following three figures out of wood.
a.
Which two figures appear to be congruent?__________________
b.
List the pairs of congruent line segments from the figures you named in part (a).________________
____________________________________________________
c.
List the pairs of congruent angles from the figures you named in part (a)._____________________
__________________________________________________________________________________
34. Ian, Isabella, Lloyd, and Jason made claims about triangles. Evaluate each of their claims. If one of the claims is
false, give an example that disproves the claim.
a.
Ian says that if the three sides of one triangle have the same length as the three sides of a second triangle,
then the two triangles are congruent._______________________________________________________
b.
Isabella says if two sides and their included angle on one triangle have the same measures as two sides
and their included angle on another triangle, then the two triangles are congruent._________________
___________________________________________________________________________________
c.
Lloyd says that if two angles and their included side on one triangle have the same measures as two
angles and their included side on another triangle, then the two triangles are congruent._____________
____________________________________________________________________________________
d.
Jason says that if the three angles on one triangle have the same measure as the three angles on another
triangle, then the triangles are congruent.__________________________________________________
____________________________________________________________________________
Determine whether it is possible to form a triangle using the set of segments with the given measurements.
Explain your reasoning.
35. 15 m, 4 m, 10.9 m ___________ ______________________________________________________________
__________________________________________________________________________________________
Determine whether it is possible to form a triangle using the set of segments with the given measurements.
Explain your reasoning
36. 7 in., 8.7 in., 15.4 in. ________ ____________________________________________________________
_______________________________________________________________________________________
7th chapter 9 & 10
Answer Section
1. ANS:
No. Line EF and
cannot be skew. Line EF must be in plane S because E and F are in plane S. Similarly,
must be in plane S because G and H are in plane S. Therefore, the two lines are coplanar, not skew.
PTS: 1
REF: 9.1
NAT: 7.G.2
TOP: Pre Test
KEY: geometry | protractor | compass | straightedge | sketch | draw | construct | geometric construction | point |
line | plane | coplanar lines | skew lines | line segment | endpoints | arc | congruent line segments | congruent |
intersection
2. ANS:
The measure of
is 44 and the measure of
is 44.
Yes. These two angles are congruent because they have the same measure.
PTS: 1
REF: 9.2
NAT: 7.G.2
TOP: Pre Test
KEY: ray | angle | sides of an angle | vertex | degrees | acute angle | right angle | obtuse angle | straight angle |
congruent angles | bisect | angle bisector
3. ANS:
The length of
is 4 units. Line segment VZ is congruent to
.
PTS: 1
REF: 9.3
NAT: 7.G.2 | 7.G.5 TOP: Pre Test
KEY: supplementary angles | complementary angles | perpendicular | midpoint of a segment | segment bisector |
perpendicular bisector | adjacent angles | linear pair | vertical angles
4. ANS:
b, a, c
PTS: 1
REF: 10.1
NAT: 7.G.2
TOP: Pre Test
KEY: Triangle Sun Theorem | remote interior angles of a triangle | Exterior Angle Theorem | Exterior Angle
Inequality Theorem
5. ANS:
The measure of
is 32, the measure of
is 62, and the measure of
is 86. Corresponding angles on
congruent figures have the same measure.
PTS: 1
REF: 10.3
NAT: 7.G.2
TOP: Pre Test
KEY: geometric figures | congruent geometric figures | corresponding sides | corresponding angles | included
angle | included side
6. ANS:
No. Points F, G, and H cannot be on the same arc of the circle with center E because the distance from a circle’s
center to any point on the same arc of the circle is the same.
PTS: 1
REF: 9.1
NAT: 7.G.2
TOP: Post Test
KEY: geometry | protractor | compass | straightedge | sketch | draw | construct | geometric construction | point |
line | plane | coplanar lines | skew lines | line segment | endpoints | arc | congruent line segments | congruent |
intersection
7. ANS:
Kevin used
to construct the new triangle.
PTS: 1
REF: 10.3
NAT: 7.G.2
TOP: Post Test
KEY: geometric figures | congruent geometric figures | corresponding sides | corresponding angles | included
angle | included side
8. ANS:
The measure of
is 32 and the measure of
is 32.
Yes. These two angles are congruent because they have the same measure.
PTS: 1
REF: 9.2
NAT: 7.G.2
TOP: Post Test
KEY: ray | angle | sides of an angle | vertex | degrees | acute angle | right angle | obtuse angle | straight angle |
congruent angles | bisect | angle bisector
9. ANS:
The measure of an angle supplementary to
is 157. The measure of an angle complementary to
is
67.
PTS: 1
REF: 9.3
NAT: 7.G.2 | 7.G.5 TOP: Post Test
KEY: supplementary angles | complementary angles | perpendicular | midpoint of a segment | segment bisector |
perpendicular bisector | adjacent angles | linear pair | vertical angles
10. ANS:
a.
Angle 3 is congruent to
because they are vertical angles. Therefore,
. Both
and
are
supplementary to 1. Both of their measures are equal to
, or
. So,
.
b.
The linear pair is
is 100.
and
, or
and
. The measure of
is 80, so the measure of both
and
PTS: 1
REF: 9.3
NAT: 7.G.2 | 7.G.5 TOP: End Ch Test
KEY: supplementary angles | complementary angles | perpendicular | midpoint of a segment | segment bisector |
perpendicular bisector | adjacent angles | linear pair | vertical angles
11. ANS:
Yes. It is possible to form a triangle because
, and 180 is greater than 97.
12.
13.
14.
15.
16.
17.
PTS: 1
REF: 10.4
NAT: 7.G.2
TOP: End Ch Test
KEY: Triangle Inequality Theorem
ANS: C
PTS: 1
REF: 9.3
NAT: 7.G.2 | 7.G.5
TOP: Standardized Test
KEY: supplementary angles | complementary angles | perpendicular | midpoint of a segment | segment bisector |
perpendicular bisector | adjacent angles | linear pair | vertical angles
ANS: B
PTS: 1
REF: 9.2
NAT: 7.G.2
TOP: Standardized Test
KEY: ray | angle | sides of an angle | vertex | degrees | acute angle | right angle | obtuse angle | straight angle |
congruent angles | bisect | angle bisector
ANS: C
PTS: 1
REF: 9.1
NAT: 7.G.2
TOP: Standardized Test
KEY: geometry | protractor | compass | straightedge | sketch | draw | construct | geometric construction | point |
line | plane | coplanar lines | skew lines | line segment | endpoints | arc | congruent line segments | congruent |
intersection
ANS: A
PTS: 1
REF: 9.2
NAT: 7.G.2
TOP: Standardized Test
KEY: ray | angle | sides of an angle | vertex | degrees | acute angle | right angle | obtuse angle | straight angle |
congruent angles | bisect | angle bisector
ANS: A
PTS: 1
REF: 9.1
NAT: 7.G.2
TOP: Standardized Test
KEY: geometry | protractor | compass | straightedge | sketch | draw | construct | geometric construction | point |
line | plane | coplanar lines | skew lines | line segment | endpoints | arc | congruent line segments | congruent |
intersection
ANS: A
PTS: 1
REF: 9.3
NAT: 7.G.2 | 7.G.5
TOP: Standardized Test
KEY: supplementary angles | complementary angles | perpendicular | midpoint of a segment | segment bisector |
perpendicular bisector | adjacent angles | linear pair | vertical angles
18. ANS: C
PTS: 1
REF: 9.2
NAT: 7.G.2
TOP: Standardized Test
KEY: ray | angle | sides of an angle | vertex | degrees | acute angle | right angle | obtuse angle | straight angle |
congruent angles | bisect | angle bisector
19. ANS: A
PTS: 1
REF: 9.3
NAT: 7.G.2 | 7.G.5
TOP: Standardized Test
KEY: supplementary angles | complementary angles | perpendicular | midpoint of a segment | segment bisector |
perpendicular bisector | adjacent angles | linear pair | vertical angles
20. ANS: A
PTS: 1
REF: 9.3
NAT: 7.G.2 | 7.G.5
TOP: Standardized Test
KEY: supplementary angles | complementary angles | perpendicular | midpoint of a segment | segment bisector |
perpendicular bisector | adjacent angles | linear pair | vertical angles
21. ANS: B
PTS: 1
REF: 9.2
NAT: 7.G.2
TOP: Standardized Test
KEY: ray | angle | sides of an angle | vertex | degrees | acute angle | right angle | obtuse angle | straight angle |
congruent angles | bisect | angle bisector
22. ANS: B
PTS: 1
REF: 9.1
NAT: 7.G.2
TOP: Standardized Test
KEY: geometry | protractor | compass | straightedge | sketch | draw | construct | geometric construction | point |
line | plane | coplanar lines | skew lines | line segment | endpoints | arc | congruent line segments | congruent |
intersection
23. ANS: C
PTS: 1
REF: 10.4
NAT: 7.G.2
TOP: Standardized Test
KEY: Triangle Inequality Theorem
24. ANS: C
PTS: 1
REF: 10.1
NAT: 7.G.2
TOP: Standardized Test
KEY: Triangle Sun Theorem | remote interior angles of a triangle | Exterior Angle Theorem | Exterior Angle
Inequality Theorem
25. ANS: B
PTS: 1
REF: 10.3
NAT: 7.G.2
TOP: Standardized Test
KEY: geometric figures | congruent geometric figures | corresponding sides | corresponding angles | included
angle | included side
26. ANS: D
PTS: 1
REF: 10.1
NAT: 7.G.2
TOP: Standardized Test
KEY: Triangle Sun Theorem | remote interior angles of a triangle | Exterior Angle Theorem | Exterior Angle
Inequality Theorem
27. ANS: A
PTS: 1
REF: 10.4
NAT: 7.G.2
TOP: Standardized Test
KEY: Triangle Inequality Theorem
28. ANS: D
PTS: 1
REF: 10.3
NAT: 7.G.2
TOP: Standardized Test
KEY: geometric figures | congruent geometric figures | corresponding sides | corresponding angles | included
angle | included side
29. ANS: D
PTS: 1
REF: 10.4
NAT: 7.G.2
TOP: Standardized Test
KEY: Triangle Inequality Theorem
30. ANS: B
PTS: 1
REF: 10.3
NAT: 7.G.2
TOP: Standardized Test
KEY: geometric figures | congruent geometric figures | corresponding sides | corresponding angles | included
angle | included side
31. ANS: B
PTS: 1
REF: 10.1
NAT: 7.G.2
TOP: Standardized Test
KEY: Triangle Sun Theorem | remote interior angles of a triangle | Exterior Angle Theorem | Exterior Angle
Inequality Theorem
32. ANS:
x  64
PTS: 1
REF: 10.1
NAT: 7.G.2
TOP: End Ch Test
KEY: Triangle Sun Theorem | remote interior angles of a triangle | Exterior Angle Theorem | Exterior Angle
Inequality Theorem
33. ANS:
a.
Figure ABCDE and figure JKLMN appear to be congruent.
b.
c.
PTS: 1
REF: 10.3
NAT: 7.G.2
TOP: End Ch Test
KEY: geometric figures | congruent geometric figures | corresponding sides | corresponding angles | included
angle | included side
34. ANS:
a.
Ian’s claim is true.
b.
Isabella’s claim is true.
c.
Lloyd’s claim is true.
d.
Jason’s claim is false. One triangle could have three angles with the same measures as the three angles of
another triangle but have sides that are twice as large as the correspondingsides on the other triangle.
PTS: 1
REF: 10.3
NAT: 7.G.2
TOP: End Ch Test
KEY: geometric figures | congruent geometric figures | corresponding sides | corresponding angles | included
angle | included side
35. ANS:
No. It is not possible to form a triangle because
, and 14.9 is not greater than 15.
PTS: 1
REF: 10.4
NAT: 7.G.2
TOP: Pre Test
KEY: Triangle Inequality Theorem
36. ANS:
Yes. It is possible to form a triangle because
, and 15.7 is greater than 15.4.
PTS: 1
REF: 10.4
KEY: Triangle Inequality Theorem
NAT: 7.G.2
TOP: Post Test