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 .

Polygon poly1 Polygon poly1: Polygon[A, B, 3] Angle α Angle α: Angle between A, B, D Angle β Angle β: Angle between A, C, D Segment f Segment f: Segment [A, B] of Polygon poly1 Segment f Segment f: Segment [A, B] of Polygon poly1 Segment g Segment g: Segment [B, C] of Polygon poly1 Segment h Segment h: Segment [C, A] of Polygon poly1 Segment h Segment h: Segment [C, A] of Polygon poly1 Segment i Segment i: Segment [B, D] Segment i Segment i: Segment [B, D] Segment i Segment i: Segment [B, D] Segment j Segment j: Segment [C, D] Segment j Segment j: Segment [C, D] Segment j Segment j: Segment [C, D] Segment k Segment k: Segment [A, D] A text1 = "A" B text2 = "B" C text3 = "C" D text4 = "D"

ABC and DBC Are Two Isosceles Triangles

ABC and DBC are two isosceles 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.

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

Triangle ABC Is Isosceles

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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