Question

ABC is a tringle if angle BAD = angle CAD and BD=CD to prove that AB=AC
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Answer 1

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NCERT Solution for Triangles

NCERT SolutionsExercise 7.1 (Page 118)

1.  In quadrilateral ACBD, AC = AD and AB bisects ∠A )see figure). Show that ΔABC ≌ ΔABD. What can you say about BC and BD?

Ans. In quadrilateral ABCD we have                  AC = AD            and AB being the bisector of ∠A.            Now, in ΔABC and ΔABD,                  AC = AD[Given]                  AB = AB[Common]∠CAB = ∠DAB [∴ AB bisects ∠CAD]            ∴ Using SAS criteria, we have                  ΔABC ≌ ΔABD.            ∴ Corresponding parts of congruent triangles (c.p.c.t) are equal.            ∴ BC = BD.

2.  ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see Figure). Prove that

     (i) ΔABD ≌ ΔBAC      (ii) BD = AC      (iii) ∠ABD = ∠BAC.

Ans. (i) In quadrilateral ABCD, we have AD = BC and                ∠DAB = ∠CBA.                In ΔABD and ΔBAC,                AD = BC[Given]                AB = BA[Common]                ∠DAB = ∠CBA[Given]                ∴ Using SAS criteria, we have ΔABD ≌ ΔBAC          (ii) ∵ ΔABD ≌ ΔBAC                ∴ Their corresponding parts are equal.                ⇒ BD = AC          (ii) Since ΔABD ≌ ΔBAC                ∴ Their corresponding parts are equal.                ⇒ ∠ABD = ∠BAC

Answer 2

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