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 Equation , Equation and AB bisects Equation (see Fig). Show that Equation .What can you say about BC and BD

Angle α Angle α: Angle between B, A, D Angle β Angle β: Angle between D, A, C Segment f Segment f: Segment [A, B] Segment f Segment f: Segment [A, B] Segment g Segment g: Segment [A, C] Segment g Segment g: Segment [A, C] Segment h Segment h: Segment [B, D] Segment j Segment j: Segment [D, C] Segment i Segment i: Segment [A, D] A text1 = "A" B text2 = "B" C text3 = "C" D text4 = "D"

: ABCD Quadrilateral, AC=AD

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

Solution:

Given: In the quadrilateral ABCD, Equation and AB bisects Equation

Prove: Equation

Now,

Equation (Common line)

Equation (Given AB bisects Equation )

Equation (By Side-Angle-Side congruent rule)

Equation (By Corresponding Parts of Congruent Triangles)

Equation

Therefore, BC and BD are of equal lengths.

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

  1. Equation

  2. Equation

  3. Equation

Solution:

Angle α Angle α: Angle between B, A, D Angle β Angle β: Angle between A, D, C Segment a Segment a: Segment [A, B] of Quadrilateral poly1 Segment b Segment b: Segment [B, C] of Quadrilateral poly1 Segment c Segment c: Segment [C, D] of Quadrilateral poly1 Segment d Segment d: Segment [D, A] of Quadrilateral poly1 Segment f Segment f: Segment [A, C] Segment g Segment g: Segment [D, B] A text1 = "A" B text2 = "B" C text3 = "C" D text4 = "D"

ABCD Is a Quadrilateral

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

Solution:

  1. In Equation

    • Equation (Common line)

    • Equation (Given)

    • Equation (Given)

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

  2. Since, Equation

    • Therefore Equation by CPCT

  3. Since, Equation

  • Therefore Equation (by Corresponding Parts of Congruent Triangles)

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