Question

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

Answer 1

Answer:

In △ABC, we have

In △ABC, we haveAB=AC⇒∠ABC=∠ACB

In △ABC, we haveAB=AC⇒∠ABC=∠ACB(angles opposite to equal sides.)

In △ABC, we haveAB=AC⇒∠ABC=∠ACB(angles opposite to equal sides.)Again in △DBC, we have

In △ABC, we haveAB=AC⇒∠ABC=∠ACB(angles opposite to equal sides.)Again in △DBC, we haveDB=DC ......... (given)

In △ABC, we haveAB=AC⇒∠ABC=∠ACB(angles opposite to equal sides.)Again in △DBC, we haveDB=DC ......... (given) ⇒∠DBC=∠DCB (angles opposite to equal sides).

In △ABC, we haveAB=AC⇒∠ABC=∠ACB(angles opposite to equal sides.)Again in △DBC, we haveDB=DC ......... (given) ⇒∠DBC=∠DCB (angles opposite to equal sides).Hence we obtain

In △ABC, we haveAB=AC⇒∠ABC=∠ACB(angles opposite to equal sides.)Again in △DBC, we haveDB=DC ......... (given) ⇒∠DBC=∠DCB (angles opposite to equal sides).Hence we obtain∠ABC−∠DBC=∠ACB−∠DCB.

In △ABC, we haveAB=AC⇒∠ABC=∠ACB(angles opposite to equal sides.)Again in △DBC, we haveDB=DC ......... (given) ⇒∠DBC=∠DCB (angles opposite to equal sides).Hence we obtain∠ABC−∠DBC=∠ACB−∠DCB.This gives

In △ABC, we haveAB=AC⇒∠ABC=∠ACB(angles opposite to equal sides.)Again in △DBC, we haveDB=DC ......... (given) ⇒∠DBC=∠DCB (angles opposite to equal sides).Hence we obtain∠ABC−∠DBC=∠ACB−∠DCB.This gives∠ABD=∠ACD. [henceproved