AnswersGeometryTriangles and Their Side Lengths

Triangles and Their Side Lengths — Quiz Answers

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1
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Iliana claims that she can construct a triangle from a 12 -inch rod, a 36 -inch rod, and a 39 point 4 -inch rod. Which statement explains whether she is correct?

A
Iliana will be able to construct a triangle because the sum of any two sides is less than the third side.
B
Iliana cannot construct a triangle because the sum of the two smaller sides will not be greater than the third side.
C
Iliana will be able to construct a triangle because the sum of any two sides is greater than the third side.
D
Iliana cannot construct a triangle because the sum of the two smaller sides will be greater than the third side.
2
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Which are the possible side lengths of a triangle?

A
3 cm, 5 cm, 9 cm
B
6 cm, 9 cm, 17 cm
C
4 cm, 8 cm, 10 cm
D
8 cm, 10 cm, 18 cm
3

A triangle has side lengths measuring 3 x cm, 7 x cm, and h cm. Which expression describes the possible values of h , in cm?

A
h is equal to 4 x
B
10 x is less than h comma h is less than 4 x
C
h is equal to 10 x
D
4 x is less than h comma h is less than 10 x
4

If triangle DEF has a 90 degrees angle at vertex cap e , which statements are true? Choose two correct answers.

A
The angle at vertex cap f is obtuse.
B
Triangle DEF is an obtuse triangle.
C
The angle at vertex cap d is obtuse.
D
The angle at vertex cap d is acute.
E
Triangle DEF is a right triangle.
5

Triangle ABC is an obtuse triangle with the obtuse angle at vertex cap b Angle cap A must be

A
congruent to angle cap c .
B
congruent to angle cap b .
C
greater than 90 degrees .
D
less than 90 degrees .
6

Triangle QRS is a right triangle with the right angle at vertex cap r The sum of m angle cap q and m angle cap s must be

A
greater than 45 degrees and less than 90 degrees .
B
greater than 90 degrees and less than 180 degrees .
C
equal to 90 degrees .
D
equal to 45 degrees .
7

A triangle has side lengths measuring 2 x plus 2 ft, x plus 3 ft, and n ft. Which expression represents the possible values of n , in feet? Express your answer in simplest terms.

A
n is equal to x minus 1
B
n is equal to 3 x plus 5
C
x minus 1 is less than n comma n is less than 3 x plus 5
D
3 x plus 5 is less than n comma n is less than x minus 1
9

Steven is cutting an 11 ft piece of lumber into three pieces to build a triangular garden. Which diagram shows a way in which he can cut the wood to create three pieces that can form a triangle?

A
Image with description A piece of wood is cut into 3 pieces. The pieces are: 2 feet, 2 feet, and 7 feet.
B
Image with description A piece of wood is cut into 3 pieces. The pieces are: 3 feet, 4 feet, 4 feet.
C
Image with description A piece of wood is cut into 3 pieces. The pieces are: 3 feet, 2 feet, and 6 feet.
D
Image with description A piece of wood is cut into 3 pieces. The pieces are: 1 foot, 4 feet, 6 feet.
10

In triangle XYZ , m angle cap z is greater than m angle cap x plus m angle cap y Which must be true about triangle XYZ ?

A
m angle cap x plus m angle cap y is less than 90 degrees
B
m angle cap y is greater than 90 degrees
C
angle cap x and angle cap y are complementary
D
m angle cap x plus m angle cap z is less than 90 degrees

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