Question

triangle ABC and triangle DBC are two isosceles triangle on the same Base BC and vertices A and D are on the same side of BC . If AD is extended to intersects BC at P, show that​

Answer 1

Correct Question :-

△ABC and △DBC are two isosceles triangle on the same Base BC and vertices A and D are on the same side of BC . If AD is extended to intersect BC at P, show that

(i) △ABD ≅ △ACD

(ii) △ABP ≅ △ACP

(iii) AP bisects ∠A as well as ∠D

(iv) AP is perpendicular bisector of BC

Solution :-

(i)△ABD ≅ △ACD

In △ABD and△ACD

AB = AC (Isosceles Traiangle)

BD = DC (Bisector)

AD = AD (Common)

∴△ABD ≅ △ACD (SSS Criteria)

(ii) △ABP ≅ △ACP

In △ABP and△ACP

AB = AC (Isosceles Traiangle)

∠ABP = ∠ACP ( Isosceles Traiangle)

AP = AP (Common)

∴ △ABP ≅ △ACP (SAS Criteria)

(iii) AP bisects ∠A as well as ∠D

∵ △ABD ≅ △ACD

∴ AP bisects ∠A as well as ∠D (CPCT)

(iv) AP is perpendicular bisector of BC

∵△ABP ≅ △ACP

∴AP is perpendicular bisector of BC (CPCT)

Answer 2

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