NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.2 – Part 3

Diagram of Isosceles Triangle: In Isosceles Triangle, the two sides are equal.

Give Isoceles Triangle that two side are same

Give Isoceles Triangle

Give Isoceles Triangle that two side are same

Q-5 ABC and DBC are two isosceles triangles on the same base BC (see Fig). Show that ABD=ACD .

Give ABC and DBC are two isoscele triangles on same base BC

Give ABC and DBC Are Two Isoscele Triangles

Give ABC and DBC are two isoscele triangles on same base BC

Solution:

Given,ABC and DBC are two isosceles triangles.

To show, ABD=ACD

  • Proof,In ΔABDandΔACD,

    AD=AD (Common)

    AB=AC (ABC is an isosceles triangle.)

    BD=CD (BCD is an isosceles triangle.)

  • Therefore, ΔABDΔACD (By SSS congruence condition).

  • Thus, ABD=ACD (By Corresponding Part of Congruent Triangles).

Q-6 ΔABC is an isosceles triangle in which AB=AC . Side BA is produced to D such that AD = AB (see Fig. 7.34). Show that BCD is a right angle.

Give triangle ABC is isosceles AB=AC,Side BA is produced to D such that AD = AB

Give Triangle ABC Is Isosceles

Give triangle ABC is isosceles AB=AC,Side BA is produced to D such that AD = AB

Solution:

Given, AB=AC and AD=AB

  • To show, BCD is a right angle.

  • Proof,In ΔABC,AB=AC (Given) ACB=ABC (Angles opposite to the equal sides are equal.)In ΔACD , AD=AB ADC=ACD (Angles opposite to the equal sides are equal.)

  • Now, In ΔABC , CAB+ACB+ABC=180°CAB+2ACB=180° CAB=180°2ACB ……………….equation(1)

  • Similarly in ΔADC , CAD=180°2ACD ……….equation(2)also, CAB+CAD=180° (BD is a straight line.)

  • Adding (i) and (ii) CAB+CAD=180°2ACB+180°2ACD 180°=360°2ACB2ACD2(ACB+ACD)=180°BCD=90°

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