NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.1 – Part 1

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Side-Angle-Side congruent

Give Side-Angle-Side congruent rule ,so ∠B=∠Y and ∠C=∠Z.so,BC=YZ

Give Side-Angle-Side Congruent Rule

Give Side-Angle-Side congruent rule ,so ∠B=∠Y and ∠C=∠Z.so,BC=YZ

Corresponding Parts of Congruent Triangles

Corresponding Parts of Congruent Triangles is ABC and A'B'C'

Give Corresponding Parts of Congruent Triangles

Corresponding Parts of Congruent Triangles is ABC and A'B'C'

Q-1 In quadrilateral , and AB bisects (see Fig). Show that .What can you say about BC and BD

: ABCD Quadrilateral, AC=AD

ABCD quadrilateral, AC=AD and bisect ∠A and also △ABC≅△ABD

Solution:

Given: In the quadrilateral ABCD, and AB bisects

Prove:

Now,

(Common line)

(Given AB bisects )

(By Side-Angle-Side congruent rule)

(By Corresponding Parts of Congruent Triangles)

Therefore, BC and BD are of equal lengths.

Q-2 ABCD is a quadrilateral in which and (see Fig.). Prove that

Solution:

ABCD is a Quadrilateral

ABCD is a quadrilateral in which AD=BC and ∠DAB = ∠CBA

Solution:

  1. In

    • (Common line)

    • (Given)

    • (Given)

    • Therefore, by Side-Angle-Side congruence condition.

  2. Since,

    Therefore by CPCT

  3. Since,

Therefore (by Corresponding Parts of Congruent Triangles)