Inequalities and Triangles

Can the sides of a triangle have lengths 3, 8, and 9?

• Yes

• No

Find the value of x by using the exterior angle theorem.

• A

• B

• C

• D

Describe the possible lengths for the third side of the triangle given the two sides 10 and 5.

• 5 < x 10

• 0 < x < 10

• 0 < x < 15

• 5 < x < 15

Order the sides from greatest to least

• a , b , c

• b , c , a

• c , b , a

• a , c , 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.

Identify the shortest side measure.

• QP

• QM

• MP

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

• yes

• no

Identify the smallest angle.

• ∠A

• ∠B

• ∠C

Identify the largest angle.

• ∠N

• ∠Q

• ∠P

Identify the longest side measure.

• LM

• MQ

• LQ