Free Printable Relationships Within Triangles

1.

Which of the following measures can be side lengths of a triangle?

a)

10, 12, 15

b)

3, 9, 12

c)

6, 6, 13

d)

5, 7, 9

2.

Given $AM=BM$ and $AC=BC$ , what is $m\angle MBC$ ?

a)

26

b)

90

c)

64

d)

13

3.

Solve for y.

a)

50

b)

25

c)

4

d)

65

4.

In the isosceles triangle $QRS$ , $\overline{RT}$ is the angle bisector of $\angle QRS$ . You want to prove the base angles of this triangle are congruent. You start by stating $\angle1\cong\angle2$ . What is a valid reason for this statement?

a)

Reflexive property of congruence

b)

Definition of angle bisector

c)

Symmetric property of congruence

d)

Corresponding angles are congruent

5.

Which of the following measures can be side lengths of a triangle?

a)

9, 1, 4

b)

6, 3, 5

c)

21, 20, 2

d)

7, 14, 7

6.

What is $m\angle B$ ?

a)

70

b)

180

c)

140

d)

40

7.

What is y?

a)

40

b)

55

c)

70

d)

110

8.

What is x?

a)

40

b)

55

c)

70

d)

110

9.

$LN=24$ , $OM=9y-43$ , and $\overline{OM}$ is a perpendicular bisector of $\overline{LN}$ .
Determine which of the following is true.

a)

y = 8

b)

LM = 12

c)

OM = 20

d)

perimeter of $\Delta MON$ = 69

e)

perimeter of $\Delta LMN\ =\ 74$

10.

X is a midpoint of $\overline{UV}$ and Y is a midpoint of $\overline{UW}$ .

a)

$\overline{VX}\ \cong\ \overline{YW}$

b)

$\overline{XU}\ \cong\ \overline{UY}$

c)

$\overline{VW}\ \cong\ \frac{1}{2}\overline{XY}$

d)

$\overline{VW}\ \parallel\ \overline{XY}$

e)

$\overline{VX}\ \cong\ \overline{XU}$

11.

In $\Delta ABC$

AB = 12
BC = 24
CA = 30
What order are the angles listed in order from smallest to largest?

a)

$\angle A,\ \angle B,\ \angle C$

b)

$\angle B,\ \angle C,\ \angle A$

c)

$\angle C,\ \angle A,\ \angle B$

d)

$\angle C,\ \angle B,\ \angle A$

12.

Find $m\angle E$ .

a)

22

b)

44

c)

79

d)

158

13.

Find YZ.

a)

YZ = 25

b)

YZ = 4

c)

Look! There it is.

d)

Not enough information. An equiangular triangle is not necessarily equilateral.

14.

Which of the following relationships are true. Select all that apply.

a)

$m\angle BAC\ =\ 2\left(m\angle BCA\right)$

b)

$\overline{AC}\ \parallel\ \overline{DE}$

c)

$AC=2DE$

d)

$m\angle BDE=m\angle BED$

15.

What additional information makes it possible to prove $\Delta ABC$ is an isosceles triangle?

a)

$\overline{AM}\ \cong\ \overline{CP}$

b)

$\overline{BM}\ \cong\ \overline{BP}$

c)

$\angle MAN\ \cong\ \angle QPC$

d)

$\Delta MAN$ is an isosceles triangle.

16.

What is UT?

a)

A line segment

b)

3

c)

15

17.

Choose the longest side of the figure.

a)

$\overline{XZ}$

b)

$\overline{XY}$

c)

$\overline{YZ}$

18.

What is the range of possible lengths of the missing side?

a)

3 < YZ < 4

b)

YZ > 7

c)

YZ = 5

d)

1 < YZ < 7

19.

Find the range of possible values for x.

a)

2.5 > x < 15

b)

2.5 < x > 15

c)

2.5 > x > 15

d)

2.5 < x < 15

20.

Given: $\Delta ABC$ with $BC\ >\ AC.$
Prove: $m\angle A\ \ne\ m\angle B$

Which of the following could be a statement in the indirect proof?

a)

By the definition of base angles of an isosceles triangle, $\angle A\ \cong\angle B$

b)

By the converse of the isosceles base angles theorem, $BC\ =\ AC.$

c)

By the definition of base angles of an isosceles triangle, $\angle B\cong\angle C.$

d)

By the converse of the hinge theorem, $m\angle A>m\angle B$

Relationships Within Triangles

Total questions: 20

Worksheet time: 5hrs 0mins

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