AnswersMO-Geometry AIncenter and Circumcenter

Incenter and Circumcenter — Unit test Answers

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21
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Triangle A B C is shown. Lines are drawn from each point to the opposite side and intersect at point D. They form line segments A G, B E, and C F.

Question illustration
A
BE, CF, and AG are angle bisectors.
B
BE ⊥ AC, AG ⊥ BC, and CF ⊥ AB.
C
BE bisects AC, CF bisects AB, and AG bisects BC.
D
BE is a perpendicular bisector of AC, CF is a perpendicular bisector of AB, and AG is a perpendicular bisector of BC.
22
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Which statements regarding the diagram of ΔEBC are true? Select three options.

A
∠BEC is an exterior angle.
B
∠DEC is an exterior angle.
C
∠ABE and ∠EBC are supplementary angles.
D
∠BCF and ∠DEC are supplementary angles.
E
∠BEC is a remote interior angle to exterior ∠BCF.
23

If isosceles triangle ABC has a 130° angle at vertex B, which statement must be true?

A
m∠A = 15° and m∠C = 35°
B
m∠A + m∠B = 155°
C
m∠A + m∠C = 60°
D
m∠A = 20° and m∠C = 30°
24

In the triangles, and .

Question illustration
A
congruent to
B
longer than
C
shorter than
D
the same length as
25

Consider the diagram.

Question illustration
A
corresponding angles theorem
B
alternate interior angles theorem
C
vertical angles theorem
D
alternate exterior angles theorem
26

Horizontal lines e and f are cut by vertical lines a and b. At the intersection of lines a and e, the uppercase right angle is (x + 1) degrees. At the intersection of lines a and f, the bottom right angle is (x minus 3) degrees. At the intersection of lines b and e, the bottom left angle is y degrees.

Question illustration
A
87
B
88
C
91
D
92
27

The given line segment has a midpoint at (3, 1).

Question illustration
A
y = x
Option A
B
y = x – 2
Option B
C
y = 3x
D
y = 3x − 8
28

Triangle KNM is shown.

Question illustration
A
KN = NM
B
KN + NM = KM
C
KM = 2(NM)
D
KN = KM
Option D
29

Which diagram shows lines that must be parallel lines cut by a transversal?

A
2 horizontal lines are intersected by a third line. At the intersection of the first line with the third line, the bottom left angle is 115 degrees. At the intersection of the second line with the third line, the uppercase left angle is 65 degrees.
Option A
B
2 horizontal lines are intersected by a third line. At the intersection of the first line with the third line, the bottom left angle is 115 degrees and the bottom right angle is 65 degrees.
Option B
C
2 horizontal lines are intersected by a third line. At the intersection of the first line with the third line, the top right angle is 115 degrees. At the intersection of the second line with the third line, the uppercase left angle is 115 degrees.
Option C
D
2 horizontal lines are intersected by a third line. At the intersection of the first line with the third line, the uppercase left angle is 65 degrees and the bottom right angle is 65 degrees.
Option D
30

Based on this information, which pair of lines, together, could be perpendicular to RS? Select two options.

A
Line E A
Option A
B
Line E R
Option B
C
Line E F
Option C
D
Line F G
Option D
E
Line F S
Option E
31

In the diagram, CE=12 units and BE=5 units.

Question illustration
A
2 units
B
7 units
C
12 units
D
17 units
32

Which must be true? Select two options.

A
Point H is the center of the circle that passes through points D, E, and F.
B
Point H is the center of the circle that passes through points L, M, and N.
C
Line segment H E is-congruent-to line segment H D
Option C
D
Line segment L H is-congruent-to line segment N H
Option D
E
Line segment F L is-congruent-to line segment F N
Option E
33

Triangle T R S has centroid Z. Lines are drawn from each point to the midpoint of the opposite side to form line segments T W, R V, and S U.

Question illustration
A
3 inches
B
6 inches
C
12 inches
D
18 inches
34

On a coordinate plane, 2 lines are shown. Line H J has points (negative 4, negative 2) and (0, 4). Line F G has points (negative 4, 1) and (0, negative 2).

Question illustration
A
They are perpendicular because their slopes are equal.
B
They are perpendicular because their slopes are negative reciprocals.
C
They are not perpendicular because their slopes are equal.
D
They are not perpendicular because their slopes are not negative reciprocals.
35

Consider triangle WXY.

Question illustration
A
Angle W is greater than angle Y.
B
Angle Y is the largest angle.
C
Angle X is smaller than angle W.
D
Angle W is the smallest angle.
36

Point X is the circumcenter of ΔABC.What is the length of XB?

Question illustration
A
4.2 cm
B
4.6 cm
C
4.8 cm
D
5.3 cm
37

Triangle A B C is shown with its exterior angles. Line C B extends through point D. Line B C extends to form exterior angle that is 135 degrees. Angle C A B is 75 degrees.

Question illustration
A
m∠ABC = 15°
B
m∠ABC = 45°
C
m∠ABC = 60°
D
m∠ABC = 75°

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