Triangle Side Lengths and Triangle Inequality

Determine whether a triangle exists based on the given side lengths. Explain.

• Yes; the third side is the longest.

• No; the sum of the length of two sides is not greater than the third.

• No; the first side is too long.

• Yes; the sum of the lengths of any two sides is greater than the third.

Which could be the lengths of the sides of ΔXYZ?

• XY = 6, YZ = 14, XZ = 8

• XY = 14, YZ = 4.7, XZ = 4.7

• XY = 8.5, YZ = 17, XZ = 10.6

• XY = 9, YZ = 12, XZ = 21

Determine the range of the third side based on the given side lengths of 18 and 29.

​ (a)   <x<​ ​ (b)  

• 11
• 47
• 6
• 23
• 32
• 63

The lengths of two sides of ΔXYZ are 16 in. and 10 in. Which could NOT be the length of the third side?

• 5

• 13

• 17

• 24

List the sides in order from largest to smallest.

• RS, ST, TR

• RS, RT, ST

• RT, TS, SR

• TR, RS, ST

Directions: Write your answer in the box. Use two letters to define each side length. List the sides in order from least to greatest.

• DF, DE, EF

• DE, DF, EF

• EF, DF, DE

• EF, DE, DF

List the angles in order from smallest to largest.

• ∠A, ∠B, ∠C

• ∠A, ∠C, ∠B

• ∠C, ∠A, ∠B

• ∠C, ∠B, ∠A

Look at the diagram showing triangles ABD and BCD. Which statement is NOT true?

• ∠1 < ∠2

• ∠5 < ∠4

• ∠3 > ∠2

• ∠6 < ∠5

Given the triangle shown, what is the measure of angle D?

• m∠D = 30°

• m∠D = 35°

• m∠D = 85°

• m∠D = 115°

What is the measure of angle ADB?