Inequalities in Triangles

Two sides of a triangle have side lengths of 17 meters and 12 meters.  What is the range of possible lengths for the third side?

• 12 < x < 17

• 12 < x < 29

• 5 < x < 17

• 5 < x < 29

• 10.5

• 15

• 21

• 28

Order the sides from greatest to least

• a , b , c

• b , c , a

• c , b , a

• a , c , b

Which of the following statements must be true?

• RS > XY

• RS < XY

• ST < XZ

Which of the following relationships is true?

• m<d > m<c

• m<d < m<a

• m<d > m<b

• m<a < m<b

In a triangle △PQR, PT bisects ∠QPR. Prove that PQ is greater than QT. Click on 'Yes' when it is completed.

• Yes

• No

Answer explanation

Since PT bisects ∠QPR, we have, ∠QPT = ∠TPR .......(1) Also, in △PTR, ∠PTQ > ∠TPR.... [As an exterior angle of a triangle is always greater than either of the interior opposite angles] Therefore, ∠PTQ > ∠QPT.....(from (1)) Since in a triangle, the greater angle has the greater side opposite to it, ∴ PQ > QT Hence, proved.

Compare measure of angle Y and measure of angle M.

• measure of angle Y = measure of angle M

• measure of angle Y > measure of angle M

• measure of angle Y < measure of angle M

• Not enough information is given.

In ∆LMN, the measure of ∠L is 51° and the measures of ∠M is 48°. Which of the following inequalities concerning the lengths of the sides of ∆LMN is true?

• MN>LM

• LN+MN<LM

• LN>MN

• LM>LN

Name the smallest angle in this triangle.

• ∠A

• ∠B

• ∠C

Select all that are TRUE.

• AB > AE

• BE > CE

• BE > CD

• CD < DE

• CE > BC