AnswersSSHS Geometry 1BTriangle Classification Theorems

Triangle Classification Theorems Answers

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3

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
6

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.
11

Two sides of an acute triangle measure 5 inches and 8 inches. The length of the longest side is unknown.What is the greatest possible whole-number length of the unknown side?

A
8 inches
B
9 inches
C
12 inches
D
13 inches
12

The shorter sides of an acute triangle are x cm and 2x cm. The longest side of the triangle is 15 cm.What is the smallest possible whole-number value of x?

A
6
B
7
C
8
D
9
13

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
14

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
15

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
16

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.
17

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
18

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
19

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.
20

Which set of numbers can represent the side lengths, in inches, of an acute triangle?

A
4, 5, 7
B
5, 7, 8
C
6, 7, 10
D
7, 9, 12

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