# NCERT Mathematics Class 9 Exemplar Ch 7 Triangles Part 5

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

8. In Fig., 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.

9. 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.

10. 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.

11. In Fig., AD is the bisector of ∠BAC. Prove that AB > BD.