NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.3 – Part 1

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Corresponding Parts of Congruent Triangle(CPCT)

Give Corresponding Parts of Congruent Triangle If two triangles ABC and PQR are congruent under the corresponding A↔p,B↔Q and it is expressed as ΔABC ≅ ΔPQR

Give Corresponding Parts of Congruent Triangle

Give Corresponding Parts of Congruent Triangle If two triangles ABC and PQR are congruent under the corresponding A↔p,B↔Q and it is expressed as ΔABC ≅ ΔPQR

CPCT means that the corresponding sides are equal and the corresponding angles are equal.

Q-1 Equation and Equation are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see Fig). If AD is extended to intersect BC at P, show that

  1. Equation

  2. Equation

  3. AP bisects Equation as well as Equation

  4. AP is the perpendicular bisector of BC.

Segment f Segment f: Segment [A, B] Segment g Segment g: Segment [B, C] Segment h Segment h: Segment [C, A] Segment i Segment i: Segment [C, D] Segment j Segment j: Segment [B, E] Segment k Segment k: Segment [E, A] A text1 = "A" B text2 = "B" C text3 = "C" D text4 = "D" P text5 = "P"

Triangle ABC and Triangle DBC Are Two Isosceles Triangles

Triangle ABC and Triangle DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC

Solution:

Given, Equation and Equation are two isosceles triangles.

  1. In Equation Equation (Common line) Equation ( Equation is isosceles) Equation ( Equation is isosceles)

    Therefore, Equation by SSS congruence condition

  2. In Equation Equation (Common line) Equation ( Equation so by CPCT) Equation ( Equation is isosceles)Therefore, Equation by SAS congruence condition.

  3. Equation by Corresponding Parts of Congruent Triangles as Equation .AP bisects Equation . ……………..equation (1)

    also,In Equation and Equation , Equation (Common line) Equation ( Equation is isosceles.) Equation ( Equation so by Corresponding Parts of Congruent Triangle(CPCT)).

    Therefore, Equation by SSS congruence condition.

    Thus, Equation by CPCT. ………….equation(2)By (1) and (2) we can say that AP bisects Equation as well as Equation .

  4. Equation (by CPCT as Equation )and Equation ……………equation(3) also, Equation (BC is a straight line.) Equation Equation ……………equation(3)

    From (1) and (2),

    AP is the perpendicular bisector of BC.

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