Free Printable Honors Geometry: Inequalities in One Triangle

1.

List the angles of the triangle in order from smallest to largest:

ΔXYZ, where XY = 12, YZ = 24, ZX = 30

a)

∡Z, ∡X, ∡Y

b)

∡X, ∡Y, ∡Z

c)

∡Z, ∡Y, ∡X

d)

∡Y, ∡Z, ∡X

2.

List the sides of the triangle in order from shortest to longest:

ΔDEF, with m∡D = 20, m∡E = 120, and m∡F = 40

a)

EF, DE, DF

b)

DE, DF, EF

c)

DF, DE, EF

d)

DF, EF, DE

3.

Can a triangle have sides with the given lengths:

4 m, 5 m, 9 m

a)

Yes

b)

No

4.

Can a triangle have sides with the given lengths?

15 cm, 1 cm, 15 cm

a)

Yes

b)

No

5.

The lengths of two sides of a triangle are 5 in and 16 in. What is the range of possible lengths for the third side?

a)

11 in < x < 21 in

b)

x > 0

c)

11 or 21

d)

5 < x < 16

6.

Find the longest side of ΔABC, with m∡A = 50, m∡B = 2x - 10, m∡C = 5x.

a)

AB

b)

BC

c)

AC

d)

∡C

7.

Name the smallest angle in this triangle.

a)

∠A

b)

∠B

c)

∠C

8.

Name the largest angle in this triangle.

a)

∠D

b)

∠E

c)

∠F

9.

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

10.

Order the sides from greatest to least

a)

a , b , c

b)

b , c , a

c)

c , b , a

d)

a , c , b

11.

Where would the largest angle of a triangle be located?

a)

Across from the longest side.

b)

Across from the shortest side

c)

I need more information to get an answer.

12.

List the SIDES from smallest to largest.

a)

$\overline{PR},\ \overline{QP},\ \overline{RQ}$

b)

$\overline{PR},\ \overline{RQ},\ \overline{QP}$

c)

$\overline{QP},\ \overline{PR},\ \overline{RQ}$

d)

$\overline{QP},\ \overline{RQ},\ \overline{PR}$

13.

Is it possible to construct a triangle with sides 15, 37, 53?

a)

Yes

b)

No

c)

Cannot be determined

14.

A triangle has two sides with lengths 5 and 13. Which choice describes the possible lengths of the third side?

a)

$7<x<16$

b)

$5<x<13$

c)

$8<x<18$

d)

$9<x<19$

15.

A triangle has side lengths 6 and 10.

Which choice CANNOT be the length of the third side?

a)

5

b)

11

c)

15

d)

17

16.

Use the figure to determine the relationship between the lengths of the given sides.

a)

DE\ <\ DG

b)

$DE\ >\ DG$

17.

Use the figure to determine the relationship between the lengths of the given sides.

a)

EG\ <\ FG

b)

$EG\ >\ FG$

Honors Geometry: Inequalities in One Triangle

Total questions: 17

Worksheet time: 1hrs 25mins

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