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 and 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. AP bisects as well as

  2. AP is the perpendicular bisector of BC.

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, and are two isosceles triangles.

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

    Therefore, by SSS congruence condition

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

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

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

    Therefore, by SSS congruence condition.

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

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

    From (1) and (2),

    AP is the perpendicular bisector of BC.