AnswersGeometry - Semester 1 PathwaysTriangles and Their Side Lengths

Triangles and Their Side Lengths Answers

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Fiona's school is in the shape of a triangle, with three hallways connecting the corners. Fiona enters the building and walks 90 yards through the first hallway to the first corner. Then, she walks 60 yards through the second hallway to the second corner.

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A
between 30 yards and 60 yards
B
between 30 yards and 90 yards
C
between 30 yards and 120 yards
D
between 30 yards and 150 yards
2
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The isosceles triangle has a base that measures 14 units.

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A
equal to 7.
B
between 7 and 14.
C
greater than 7.
D
between 14 and 28.
3

Which statements about the diagram are true? Select three options.

A
D E + E F greater-than D F
Option A
B
is an isosceles triangle.
Option B
C
5 less-than D F less-than 13
Option C
D
D E + D F less-than E F
Option D
E
is a scalene triangle.
Option E
4

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

A
4x < h < 10x
B
10x < h < 4x
C
h = 4x
D
h = 10x
5

In triangle XYZ, m∠Z > m∠X + m∠Y. Which must be true about △XYZ?

A
m∠X + m∠Z < 90°
B
m∠Y > 90°
C
∠X and∠Y are complementary
D
m∠X + m∠Y < 90°
6

Iliana claims that she can construct a triangle from a 12-inch rod, a 36-inch rod, and a 39.4-inch rod. Which statement explains whether she is correct?

A
Iliana cannot construct a triangle because the sum of the two smaller sides will not be greater than the third side.
B
Iliana cannot construct a triangle because the sum of the two smaller sides will 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 will be able to construct a triangle because the sum of any two sides is less than the third side.
7

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
A piece of wood is cut into 3 pieces. The pieces are: 2 feet, 2 feet, and 7 feet.
Option A
B
A piece of wood is cut into 3 pieces. The pieces are: 1 foot, 4 feet, 6 feet.
Option B
C
A piece of wood is cut into 3 pieces. The pieces are: 3 feet, 2 feet, and 6 feet.
Option C
D
A piece of wood is cut into 3 pieces. The pieces are: 3 feet, 4 feet, 4 feet.
Option D
8

Which are the possible side lengths of a triangle?

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

Triangle ABC is an obtuse triangle with the obtuse angle at vertex B. Angle A must be

A
less than 90°.
B
greater than 90°.
C
congruent to angle B.
D
congruent to angle C.
10

For a craft project, four students each chose three pieces of wire from a box.Don’s wires measure 3 inches, 5 inches, and 12 inches.Margo’s wires measure 6 inches, 8 inches, and 14 inches.Sonji’s wires measure 12 inches, 8 inches, and 17 inches.Liam’s wires measure 16 inches, 8 inches, and 27 inches.

A
Don
B
Margo
C
Sonji
D
Liam

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