2. In DABC , ∠Q > ∠R, PA is the bisector of ∠QPR and PM ^QR. Prove that <∠APM = 1/2(∠< Q – ∠<R).

3. D ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. Show that ∠BCD is a right angle.

4. In a right angled triangle, one acute angle is double the other. Prove that the hypotenuse is double the smallest side.

6. Example 5. If the bisector of the vertical angle of a triangle bisects the base, prove that the triangle is isosceles.

7. A triangle ABC is right angled at A. L is a point on BC such that AL ^ BC. Prove that ∠ < BAL = ∠ < ACB

8. Q is a point on the side SR of a Δ PSR such that PQ = PR. Prove that PS > PQ.

9. S is any point on side QR of a Δ PQR. Show that: PQ + QR + RP > 2 PS.

10. D is any point on side AC of a Δ ABC with AB = AC. Show that CD < BD.

11. l || m and M is the mid-point of a line segment AB. Show that M is also the mid-point of any line segment CD, having its end points on l and m, respectively.

12. Bisectors of the angles B and C of an isosceles triangle with AB = AC intersect each other at O. BO is produced to a point M. Prove that ∠MOC =∠ABC.

13. Bisectors of the angles B and C of an isosceles triangle ABC with AB = AC intersect each other at O. Show that external angle adjacent to ∠ABC is equal to ∠BOC.

14. S is any point in the interior of Δ PQR. Show that SQ + SR < PQ + PR. {Produce QS to intersect PR at T}

15. Prove that in a right triangle, hypotenuse is the longest (or largest) side.

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