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SAI International School
CLASS - IX

Mathematics
Chapter-7: Triangles
Assignment -4

Sub-Topic: Inequalities in a Triangle

1 In ∆PQR, if ∠R >∠Q, then
(a) QR > PR (b) PQ > PR
(c) PQ < PR (d) QR < PR

2. In ∆PQR, P = 70° and ∠R = 30°. Which side of this triangle is the longest?
Give reasons for your answer.

3. AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2AD?
Give reason for your answer.

4. Prove that the angle opposite to the greatest side of a triangle is greater than
o
two third of a right angle i.e., greater than 60 .

5. In ABC, AD is a median then prove that AB + AC > 2 AD.

6. In an isosceles triangle ABC, AB = AC and CB is produced to D.
Prove that AD > AC.

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7. In PQR side QP is produced to D so that QD = QR and P = 70 , and
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Q = 60 , prove that :
(i) PD < RD
|(ii) PD < PR

8. In the given figure AB < BC, BD is the bisector of∠ABC.
Prove that : BDC > ADB