AnswersGeometry - Semester 1 PathwaysIncenter and Circumcenter

Incenter and Circumcenter — Unit test Answers

14 verified answers2 views
1
Free Preview

Triangle J K L is shown. Lines are drawn from each point to the opposite side and intersect at point P. Line segments J O, K M, and L N are created.

Question illustration
A
LN ⊥ JK, JO ⊥ LK, and JL ⊥ MK.
B
JL = LK = KJ
C
JM = ML, LO = OK, and KN = NJ.
D
LN is a perpendicular bisector of JK, JO is a perpendicular bisector of LK, and MK is a perpendicular bisector of JL.
2
Free Preview

In triangle QRS, QR = 8 and RS = 5. Which expresses all possible lengths of side QS?

Q
QS = 13
5
5 < QS < 8
Q
QS > 13
3
3 < QS < 13
3

The base angle of an isosceles triangle measures 54°. What is the measure of its vertex angle?

2
27°
3
36°
5
54°
7
72°
4

[Figure may not be drawn to scale]

Question illustration
A
12 mm
B
24 mm
C
36 mm
D
48 mm
5

[Figure may not be drawn to scale]

Question illustration
A
25 units
B
50 units
C
100 units
D
150 units
6

is the angle bisector of YEX and the perpendicular bisector of . is the angle bisector of YGZ and the perpendicular bisector of . is the angle bisector of ZFX and the perpendicular bisector of . Point A is the intersection of , , and .

Question illustration
A
Point A is the center of the circle that passes through points E, F, and G but is not the center of the circle that passes through points X, Y, and Z.
B
Point A is the center of the circle that passes through points X, Y, and Z but is not the center of the circle that passes through points E, F, and G.
C
Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.
D
Point A is not necessarily the center of the circle that passes through points E, F, and G or the center of the circle that passes through points X, Y, and Z.
7

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

Question illustration
A
Point G cannot be the centroid because 18:6 does not equal 2:1.
B
Point G cannot be the centroid because FG should be longer than CG.
C
Point G can be the centroid because 12:6 equals 2:1.
D
Point G can be the centroid because FC is longer than FG.
8

Triangle B C D is shown. Line D B extends through point A to form exterior angle A B C. Angle B D C is 67 degrees and Angle C D B is 60 degrees.

Question illustration
A
m∠ABC = 60°
B
m∠ABC = 67°
C
m∠ABC = 120°
D
m∠ABC = 127°
9

A triangle with exterior angles is shown. The bottom right angle of the triangle is (3 h + 18) degrees. The bottom right exterior angle is (15 h) degrees.

Question illustration
A
h = 1.5
B
h = 9
C
h = 10
D
h = 13.5
10

Which type of triangle will always have a perpendicular bisector that is also an angle bisector?

A
right
B
scalene
C
obtuse
D
equilateral
11

Jace is making a water play table from a triangular table top. He sketched a dotted line to show where he wants to add a circular water bowl. It should go all the way to the edges of the table as shown.

Question illustration
A
He should find the midpoint of each edge of the table.
B
He should bisect each of the angles at the vertices of the triangular table top.
C
He should draw perpendicular lines through any point along the edges of the table.
D
He should draw perpendicular line segments from each corner to the opposite edge of the table.
12

Consider the triangle shown.

Question illustration
A
Line segment P Q, line segment R Q, line segment R P
Option A
B
Line segment R Q, Line segment P Q, line segment P Q
Option B
C
Line segment R Q, line segment R P, line segment P Q
Option C
D
Line segment R P, line segment P Q, line segment R Q
Option D
13

Equilateral triangle ABC has a perimeter of 96 millimeters. A perpendicular bisector is drawn from angle A to side at point M.What is the length of ?

Question illustration
A
16 mm
B
24 mm
C
32 mm
D
48 mm
14

Point Z is the circumcenter of ΔTUV.

Question illustration
A
23.7°
B
32.8°
C
33.5°
D
57.2°
15

Triangle ABC has the angle measures shown.

Question illustration
A
Measure of angle A = 20 degrees
Option A
B
Measure of angle B = 60 degrees
Option B
C
are complementary
Option C
D
Measure of angle A + measure of angle C = 120 degrees
Option D

Did you find these answers helpful?

More from this Course

Quiz
15 verified answers

Unit Test

Quiz
15 verified answers

Unit Test

Quiz
15 verified answers

Unit Test

Incenter and Circumcenter — Unit test Answers —…