# NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.1 – Part 2

Angle Angle Side congruence condition

If two pairs of angles of two triangles are equal in measurement, and a pair of corresponding non-included sides are equal in length, then the triangles are congruent.

Angle-Side-Angle congruence condition

Triangles are congruent if any two angles and their side are equal in both triangles.

Q-3 AD and BC are equal perpendiculars to a line segment AB (see Fig.). Show that CD bisects AB

Solution:

Given,

AD and BC are equal perpendiculars to AB.

To prove,

CD bisects AB

Proof,

and *,*

(Perpendicular)

(Vertically opposite angles)

(Given)

Therefore, (by Angle Side congruence condition).

Now,

(Corresponding Part of Congruent Triangle). CD bisects AB.

Q-4 l and m are two parallel lines intersected by another pair of parallel lines p and q (see Fig). Show that

image title: l and m are intersected by p and q

image description: Figure for question l and m are two parallel lines intersected by another pair of parallel lines p and q

Solution:

Given,

and

To prove,

Proof,

In and ,

(Alternate interior angles)

(Common line)

(Alternate interior angles)

Therefore, (by Angle-Side-Angle congruence condition.)