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SAI International School
CLASS - IX

Mathematics
Chapter-7: Triangles
Home Assignment-3

Sub Topic: Some more criteria for congruence of Triangles(SSS,RHS)

1. ABCD is a quadrilateral in which AB = BC and AD = CD. Show that
BD bisects both the angles ABC and ADC

2. Two lines l and m intersect at the point O and P is a point on a line n passing
through the point O such that P is equidistant from l and m. Provethat n is the
bisector of the angle formed by l and m.

3 ABCD is a parallelogram. If its diagonals are equal, find the measure of
∠ABC.

4 Prove that if two isosceles triangles have a common base, the line joining their
vertices bisects them at right angles.
5. If two isosceles triangles have a common base, prove that the line joining their
vertices bisects the common base at right angle.

6. E is the mid-point on the side BC of a ABC, such that the perpendiculars
from E on the sides AB and AC are equal. Show that:
(i) AE bisects BAC
(ii) AC = AB.