AnswersMFISD GEOMETRY A 22-23 CRTest

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An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.Which best describes the range of possible values for the third side of the triangle?

A
x 18.9
B
12.5 < x < 18.9
C
x 26
D
6 < x < 26
22
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Which best explains whether a triangle with side lengths 2 in., 5 in., and 4 in. is an acute triangle?

A
The triangle is acute because 22 + 52 > 42.
B
The triangle is acute because 2 + 4 > 5.
C
The triangle is not acute because 22 + 42 < 52.
D
The triangle is not acute because 22 < 42 + 52.
23

Triangle A B C is shown. Lines are drawn from each point to the opposite side and intersect at point D.

Question illustration
A
Point D can be the orthocenter because it is the point of intersection of three segments coming from the vertices of the triangle.
B
Point D can be the orthocenter because each vertex angle appears to be bisected.
C
Point D cannot be the orthocenter because the orthocenter of an obtuse triangle is located outside the triangle.
D
Point D cannot be the orthocenter because the orthocenter of an obtuse triangle is located on the perimeter of the triangle.
24

Point Y is the circumcenter of triangle DEF.

Question illustration
A
Point Y is the center of the circle that passes through points D, F, and N.
B
Point Y is the center of the circle that passes through points M, N, and E.
C
Point Y is the center of the circle that passes through points L, M, and N.
D
Point Y is the center of the circle that passes through points D, E, and F.
25

Two sides of an obtuse triangle measure 12 inches and 14 inches. The longest side measures 14 inches.What is the greatest possible whole-number length of the unknown side?

A
2 inches
B
3 inches
C
7 inches
D
9 inches
26

Which set of numbers can represent the side lengths, in centimeters, of a right triangle?

A
8, 12, 15
B
10, 24, 26
C
12, 20, 25
D
15, 18, 20
27

The figure shows a circle inscribed in a triangle.

Question illustration
A
A circle was constructed using the intersection of the angle bisectors as the center of the circle and the obtuse vertex as a point on the circumference of the circle.
B
A circle was constructed using a vertex as the center of the circle and the intersection of the angle bisectors as a point on the circumference of the circle.
C
Segments perpendicular to the sides of the triangle through the intersection of the angle bisectors were constructed.
D
Segments bisecting each side of the triangle were constructed through the intersection of the angle bisectors.
28

Point P is the incenter of ΔRST.

Question illustration
A
Line segment C P is-congruent-to line segment R P
Option A
B
Line segment B P is-congruent-to line segment P C
Option B
C
PSC PTC
Option C
D
BPS APT
Option D
29

An acute triangle has two sides measuring 8 cm and 10 cm. What is the best representation of the possible range of values for the third side, s?

A
2 < s < 18
B
6 < s < 12.8
C
s 18
D
s 12.8
30

The steps shown can be used to prove that the medians of a triangle meet at a point.1. Define segments BD and CE as medians of triangle ABC.2. Write linear equations for and .3. Use a system of linear equations to solve for the coordinates of intersection point G.4. Write the equation of .5. Write an expression for the midpoint of BC, point F. 6. Show that point F lies on .7. ?

Question illustration
A
Write a linear equation for each side of the triangle.
B
Write an expression for the midpoint of AC and BC.
C
Show that AF is congruent to BD and CE.
D
Show that AF is the median of BC.
31

The longest side of an acute isosceles triangle is 8 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?

A
4.0 cm
B
4.1 cm
C
5.6 cm
D
5.7 cm
32

An orthocenter is the intersection of three

A
angle bisectors in a triangle.
B
altitudes in a triangle.
C
medians in a triangle.
D
perpendicular bisectors in a triangle.
33

Arielle is building the wooden framework for the roof of a house. She needs the angle created by the vertical and horizontal boards of the frame to be a right angle. The height of the vertical board is 12 feet. The length of the horizontal board is 15 feet. The support beam that will connect the ends of the two boards measures 20 feet.

A
It is an acute triangle. About 0.8 foot needs to be removed from the 20-foot board to create a right triangle.
B
It is an obtuse triangle. About 0.8 foot needs to be removed from the 20-foot board to create a right triangle.
C
It is an acute triangle. About 7 feet need to be removed from the 20-foot board to create a right triangle.
D
It is an obtuse triangle. About 7 feet need to be removed from the 20-foot board to create a right triangle.
34

In which figure is point G an orthocenter?

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. The lines cut 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 the lines intersect at point G.
Option D
35

Two sides of an obtuse triangle measure 9 inches and 14 inches. The length of longest side is unknown.What is the smallest possible whole-number length of the unknown side?

A
16 inches
B
17 inches
C
24 inches
D
25 inches
36

In triangle DEF, CG = (x + 5) units and DG = (3x - 2) units.[Figure may not be drawn to sacle]

Question illustration
A
12 units
B
17 units
C
34 units
D
51 units

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