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Joey is building a frame for a sandbox. The sandbox is going to be a quadrilateral that has the lengths shown.

Question illustration
A
a rectangle, because angle C is a right angle
B
a rectangle, because angle C and angle X are congruent
C
a quadrilateral, because angle C and angle X are acute
D
a quadrilateral, because angle C and angle X are obtuse
4

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
6

In which figure is point G a centroid?

A
Triangle A B C is a right triangle. Lines are drawn from each point to the opposite side and intersect at point G.
Option A
B
Triangle F D E is shown. Lines are drawn from each point to the opposite side and intersect at point G. Each line segment splits each side into 2 equal parts.
Option B
C
Triangle L M N is shown. Lines are drawn from each point to the opposite side and intersect at point G. Each angle has a different measure.
Option C
D
Triangle H J K is shown. Lines are drawn from each point to the opposite side to form right angles and they intersect at point G.
Option D
9

Point Z is the circumcenter of ΔLMN.

Question illustration
A
Line segment A N is-congruent-to line segment L B
Option A
B
Line segment N C is-congruent-to line segment B Z
Option B
C
BMZ CMZ
Option C
D
ZBM ZCM
Option D
10

Which classification best represents a triangle with side lengths 10 in., 12 in., and 15 in.?

A
acute, because 102+122>152
B
acute, because 122+152>102
C
obtuse, because 102+122>152
D
obtuse, because 122+152>102
11

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.
18

Point H is the circumcenter of ΔJKL.

Question illustration
A
Line segment F H is-congruent-to line segment D H
Option A
B
Line segment J F is-congruent-to line segment L H
Option B
C
Line segment J H is-congruent-to line segment L H
Option C
D
Line segment K F is-congruent-to line segment L D
Option D
19

Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?

A
acute, because 62 + 102 < 122
B
acute, because 6 + 10 > 12
C
obtuse, because 62 + 102 < 122
D
obtuse, because 6 + 10 > 12

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