Question

In Fig. AB = AC and AD is the bisector of ∠BAC.
(i)State three pairs of equal parts in triangles ADB and ADC.
(ii) Is ΔADB ≅ΔADC? Give reasons.
(iii)Is ∠B = ∠C? Give reasons.

Answer 1

Given :- In Fig. AB = AC and AD is the bisector of ∠BAC.

To Find :-

(i)State three pairs of equal parts in triangles ADB and ADC.

(ii) Is ΔADB ≅ΔADC ? Give reasons.

(iii)Is ∠B = ∠C ? Give reasons.

Solution :-

(i) The three pairs of equal parts in ∆ADB and ∆ADC are :-

→ AB = AC (Given.)

→ ∠BAD = ∠CAD (AD is the bisector of ∠BAC.)

→ AD = AD (common.)

so,

→ ∆ADB ≅ ∆ADC (By SAS congruence.)

therefore, (ii) is correct .

now,

→ ∠B = ∠C (By CPCT.)

hence, (iii) also correct .

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Answer 2

Given :  AB = AC and AD is the bisector of ∠BAC.

To Find :

(i) State three pairs of equal parts in triangles ADB and ADC.

(ii) Is ΔADB ≅ΔADC  

(iii)Is ∠B = ∠C  

Solution :  

The three pairs of equal parts in ∆ADB and ∆ADC are :-

  AB = AC (Given.)

 ∠BAD = ∠CAD (AD is the bisector of ∠BAC.)

  AD = AD (common.) - reflexive property

ΔADB ≅ΔADC (  SAS )   YES

   ∠B = ∠C (  CPCT )      YES

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