ABC is an isosceles triangle with AB = BC and AD ⊥ BC In ΔABD and â ‹ΔACD (i) - Maths - The Triangle and its Properties

Question

ABC is an isosceles triangle with AB = BC and AD ⊥ BC In
ΔABD and â€‹ΔACD
(i) Show three pairs of equal parts giving reason
(ii) Is â€‹ΔADB ≅
â€‹ΔADC? Give reason
(iii) Is ∠BAD = â€‹∠CAD? Give reason

Manbar Singh · Accepted Answer

i
In ∆ABD and ∆ACD,∠ADB = ∠ADC   as, AD⊥BCAB = AC   GivenAD = AD   Commonii
In ∆ABD and ∆ACD,   ∠ADB = ∠ADC   90° each, as, AD⊥BCAB = AC   GivenAD = AD   Common⇒∆ABD ≅ ∆ACD   RHSiii
Since,  ∆ABD ≅ ∆ACD   RHS⇒∠BAD = ∠CAD  CPCT

ABC is an isosceles triangle with AB = BC and AD ⊥ BC. In ΔABD and ​ΔACD (i) Show three pairs of equal parts giving reason. (ii) Is ​ΔADB ≅ ​ΔADC? Give reason. (iii) Is ∠BAD = ​∠CAD? Give reason.

ABC is an isosceles triangle with AB = BC and AD ⊥ BC. In ΔABD and ΔACD
(i) Show three pairs of equal parts giving reason.
(ii) Is ΔADB ≅ ΔADC? Give reason.
(iii) Is ∠BAD = ∠CAD? Give reason.