AnswersGeometry VIA Fall 26 clyonssdale.orgTriangles and Their Side Lengths

4.6 Triangles and Their Side Lengths Answers

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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
2
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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.
3

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
4

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.
5

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
6

Triangle QRS has the angle measures shown.

Question illustration
A
18
B
54
C
108
D
216
7

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
8

3 connecting lines are shown. Line A B is horizontal. Line A C is about half the length of A B. Line B C is about one-third of the length of A B.

Question illustration
A
AC + AB > CB
B
AC + CB < AB
C
AC + CB > AB
D
AC + AB < CB
9

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

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