Question

in figure, AB = AC and <1 = <2. Is A️ABD = ️ACD? (Give reason) ​

Answer 1

Answer:

Proved below

Step-by-step explanation:

a- angle1=angle2. (given)

ab=ac. (given)

ad=ad (common)

therefore,by SAS

∆ABD=~∆ACD

b. angle ABD= angle ACD (by cpct)

c. also by cpct

d. as ∆ABC is an isoscele triangle therefore angle opposite to equal side are equal

now, we know that angle ABD=ACD ( by cpct)

therefore,angle ABC-ABD=ABC-ACD

therefore,angle DBC=DCB

Answer 2

In ∆ACD and ∆ABD

➝ AB = AC (given)

➝ ∠1 = ∠2 (given)

➝ AD = AD (common)

Therefore,

∆ACD ≅ ∆ABD (by S.A.S congruence criterion)