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 Angle Side congruence condition of ΔENR and ΔRNV

Angle Angle Side Congruence Condition

Angle Angle Side congruence condition of ΔENR and ΔRNV

Angle-Side-Angle congruence condition

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

Angle-Side-Angle congruence condition and two triangle of ABC and XYZ

Angle-Side-Angle Congruence Condition

Angle-Side-Angle congruence condition and two triangle of ABC and XYZ

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

Figure describes the questions where AD and BC are perpendicular to AB

AD and BC Are Perpendicular to AB

Figure describes the questions where AD and BC are perpendicular to AB

Solution:

Given,

AD and BC are equal perpendiculars to AB.

To prove,

CD bisects AB

Proof,

ΔAOD and ΔBOC ,

A=B (Perpendicular)

AOD=BOC (Vertically opposite angles)

AD=BC (Given)

Therefore, ΔAODΔBOC (by Angle Side congruence condition).

Now,

AO=OB (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 ΔABCΔCDA

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

L and M Are Intersected by P and Q

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

Solution:

Given,

lm and pq

To prove,

ΔABCΔCDA Proof,

In ΔABC and ΔCDA ,

BCA=DAC (Alternate interior angles)

AC=CA (Common line)

BAC=DCA (Alternate interior angles)

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

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