Free Printable Triangle Inequalities and Converse of Pythagorean Theorem

1.

The dotted line represents a ?...

a)

median

b)

centroid

c)

midsegment

d)

midpoint

2.

The figure is an example of a(n) ...

a)

altitude

b)

perpendicular bisector

c)

midsegment

d)

angle bisector

3.

Which of the following segments represents an altitude?

a)

BX

b)

AZ

c)

AC

d)

BZ

4.

The smallest angle would be located where in a triangle?

a)

Across from the smallest side.

b)

Across from the largest side

c)

Cannot tell

5.

Where would the largest side of a triangle be located?

a)

Across from the largest angle.

b)

Across from the smallest angle.

c)

Next to the smallest side.

d)

Across the smallest side.

6.

Name the angles from SMALLEST to LARGEST

a)

Q, R, P

b)

P, Q, R

c)

R, P, Q

d)

R, Q, P

7.

Name the sides from SMALLEST to LARGEST

a)

RS, ST, TR

b)

ST, RT, RS

c)

RT, ST, RS

d)

RT, RS, ST

8.

Name the angles from LARGEST to SMALLEST

a)

R, S, T

b)

S, T, R

c)

S, R, T

d)

T, S, R

9.

Name the sides from LARGEST to SMALLEST

a)

KJ, KH, JH

b)

JH, KH, KJ

c)

KH, KJ, JH

d)

KH, JH, KJ

10.

Find the largest angle in Δ PRQ

a)

∠R

b)

∠P

c)

∠Q

d)

∠S

11.

Find the largest side in Δ BCD

a)

Segment BC

b)

Segment DB

c)

Segment DC

d)

Segment AB

12.

Use the figure to determine which of the following angles has the greatest measure: $\angle\ 1,\ \angle\ 3,\ \angle4$

a)

$\angle1$

b)

$\angle3$

c)

$\angle4$

d)

Not enough information

13.

Use the figure to determine which of the following angles has the greatest measure: $\angle\ 4,\ \angle\ 8,\ \angle9$

a)

$\angle4$

b)

$\angle8$

c)

$\angle9$

d)

Not enough information

14.

SPORTS The figure shows the position of three trees on one part of a disc golf course. At which tree position is the angle between the trees the greatest?

a)

Tree 1

b)

Tree 2

c)

Tree 3

15.

Use the Exterior Angle Inequality Theorem to list all angles that satisfy the stated condition: measures are less than $\angle1$

a)

$\angle3,\ \angle4,\ \angle5,\ \angle7,\ \angle8$

b)

$\angle3,\ \angle4,\ \angle5,\ \angle6,\ \angle8$

c)

$\angle2,\ \angle6,\ \angle7,\ \angle8$

d)

$\angle2,\ \angle6,\ \angle8,\ \angle9$

16.

Use the Exterior Angle Inequality Theorem to list all angles that satisfy the stated condition: measures are less than $\angle3$

a)

$\angle2,\ \angle6,\ \angle8,\ \angle9$

b)

$\angle1,\ \angle6,\ \angle8$

c)

$\angle5,\ \angle7,\ \angle8$

d)

$\angle2,\ \angle4,\ \angle7,\ \angle8$

17.

Which of ∠2, ∠4, and ∠6 has the largest measure?

a)

∠2

b)

∠4

c)

∠6

18.

Which of ∠4, ∠5, and ∠1 has the largest measure?

a)

∠4

b)

∠5

c)

∠1

19.

Which of ∠1, ∠7, and ∠2 has the largest measure?

a)

∠1

b)

∠7

c)

∠2

20.

Using the figure, choose the correct symbol to be used.

∠7 _____ ∠2

a)

<

b)

>

c)

=

21.

Can the following side measures form a triangle?
3, 5, 8

a)

Yes

b)

No

22.

Which of the following sets of side lengths could produce a triangle. SELECT ALL THAT APPLY.

a)

4, 4, 4

b)

5, 5, 10

c)

3, 6, 9

d)

5, 7, 11

e)

13, 5, 6

23.

Will these line segments form a triangle?

a)

yes

b)

no

24.

Which set of side lengths will form a triangle?

a)

3, 6, 12

b)

7, 7, 14

c)

9, 9, 9

d)

13, 6, 7

25.

Determine if it is possible to form a triangle with the given side lengths. 15 in., 12 in., 2 in.

a)

yes

b)

no

26.

Determine if it is possible to form a triangle with the given side lengths. 7 yd, 8 yd, 9 yd

a)

yes

b)

no

27.

9. Which of these lengths CANNOT represent the sides of a triangle?

a)

32, 34, 60

b)

28, 30, 58

c)

13, 20, 27

d)

2, 4, 5

28.

Will these three sides form a triangle?

a)

yes

b)

no

29.

Which of the following sets of side lengths could produce a triangle. SELECT ALL THAT APPLY.

a)

4, 4, 4

b)

5, 5, 10

c)

3, 6, 9

d)

5, 7, 11

e)

13, 5, 6

30.

What is a possible third side to a triangle with side lengths of 13 and 4?

a)

9

b)

12

c)

8

d)

5

31.

What is the range of values of x for a triangle's third side given side measures of 8 and 15?

a)

between 8 and 15

b)

between 7 and 23

c)

less than 7, greater than 23

32.

What is the range of values of x for a triangle's third side given side measures of 4 and 12?

a)

between 8 and 16

b)

less than 4, greater than 12

c)

between 4 and 12

33.

Given are the lengths of two sides of a triangle. Find the range of lengths for the third side. 7 ft, 13 ft

a)

more than 6 but less than 20

b)

more than 20 but less than 6

c)

less than 6 but more than 20

34.

Given are the lengths of two sides of a triangle. Find the range of lengths for the third side. 7 mm, 4 mm

a)

more than 3 but less than 11

b)

more than 11 but less than 3

c)

less than 3 but more than 11

35.

In triangle ABC, the length of side AB is 10 inches and the length of side BC is 17 inches. Which of the following could be the length of side AC?

a)

16 inches

b)

5 inches

c)

32 inches

d)

29 inches

36.

The lengths of two sides are given (8, 5). What are the possible length of the third side? Between what two numbers

a)

Between 5 and 8

b)

Between 3 and 13

c)

Between 3 and 5

d)

Between 5 and 13

37.

The lengths of two sides are given (9, 2). What are the possible length of the third side? Between what two numbers

a)

Between 0 and 2

b)

Between 2 and 9

c)

Between 7 and 11

38.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

39.

What is the formula for Pythagorean theorem?

a)

a²⁺b²=c²

b)

a+b=c

c)

a-b=c

d)

c-a=c

40.

What is the longest side of a right triangle called?

a)

Leg A

b)

Leg B

c)

Hypotenuse

d)

Pythagoras' Big Buddy

41.

Given the 3 lengths of a triangle are 6 in, 8 in and 10 in. Will this make a right triangle?

a)

yes

b)

no

42.

Do the segment lengths 15, 9 and, 12 form a right triangle?

a)

Yes

b)

No

43.

If the sides of a triangle are 7, 25, and 24, is it a right triangle?

a)

yes

b)

no

44.

Is this triangle a right triangle?

a)

yes

b)

no

45.

What do you call a singing computer?

a)

Adele

b)

Pick the other one.

Triangle Inequalities and Converse of Pythagorean Theorem

Total questions: 45

Worksheet time: 11hrs 15mins

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