Geometry Triangle Inequalities

Find the largest side in Δ BCD

• Segment BC

• Segment DB

• Segment DC

• Segment AB

• <

• >

• =

• >

• <

• =

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

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.

Tags

CCSS.HSG.CO.C.9

Which is the range of values of "x" for the triangle shown?

Which is the range of values of "x" for the triangle shown?

Name the angles from SMALLEST to LARGEST

• Q, R, P

• P, Q, R

• R, P, Q

• R, Q, P

Name the sides from SMALLEST to LARGEST

• RS, ST, TR

• ST, RT, RS

• RT, ST, RS

• RT, RS, ST

Can a triangle be formed with side lengths:
4, 7, 10

• yes

• no

• not enough information