AnswersGeometry - Semester 1 PathwaysTriangles and Their Side Lengths

Triangles and Their Side Lengths Answers

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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
2
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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
3

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
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

If triangle DEF has a 90° angle at vertex E, which statements are true? Select two options.

A
Triangle DEF is an obtuse triangle.
B
The angle at vertex D is acute.
C
The angle at vertex F is obtuse.
D
Triangle DEF is a right triangle.
E
The angle at vertex D is obtuse.
6

3 connecting lines are shown. Line D F is horizontal. Line D E is about half the length of line D F. Line F E is about one-third of the length of line D F.

Question illustration
A
EF + FD > DE
B
ED + EF < DF
C
ED + EF > DF
D
EF + FD < DE
7

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.
8

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.
9

Triangle A B C is shown. Side A B has a length of 12. Side B C has a length of x. Side A C has a length of 15.

Question illustration
A
0
B
1
C
3
D
7
10

Triangle QRS has the angle measures shown.

Question illustration
A
18
B
54
C
108
D
216

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