Question -
Answer -
Given : In тИЖABC, AB = AC
BD and CE are the bisectors of тИаB and тИаC respectively
To prove : BD = CE
Proof: In тИЖABC, AB = AC
тИ┤ тИаB = тИаC (Angles opposite to equal sides)
тИ┤┬а ┬атИаB =┬а тИаC
┬аGiven : In тИЖABC, AB = AC
BD and CE are the bisectors of тИаB and тИаC respectively
To prove : BD = CE
Proof: In тИЖABC, AB = AC
тИ┤ тИаB = тИаC (Angles opposite to equal sides)
тИ┤┬а ┬атИаB =┬а тИаC
┬аGiven : In тИЖABC, AB = AC
BD and CE are the bisectors of тИаB and тИаC respectively
To prove : BD = CE
Proof: In тИЖABC, AB = AC
тИ┤ тИаB = тИаC (Angles opposite to equal sides)
тИ┤┬а┬а
┬атИаB =┬а┬атИаC ┬а
тИаDBC = тИаECB
Now, in тИЖDBC and тИЖEBC,
BC = BC (Common)
тИаC = тИаB (Equal angles)
тИаDBC = тИаECB (Proved)
тИ┤ тИЖDBC тЙЕ тИЖEBC (ASA axiom)
тИ┤ BD = CE
тИаDBC = тИаECB
Now, in тИЖDBC and тИЖEBC,
BC = BC (Common)
тИаC = тИаB (Equal angles)
тИаDBC = тИаECB (Proved)
тИ┤ тИЖDBC тЙЕ тИЖEBC (ASA axiom)
тИ┤ BD = CE
тИаDBC = тИаECB
Now, in тИЖDBC and тИЖEBC,
BC = BC (Common)
тИаC = тИаB (Equal angles)
тИаDBC = тИаECB (Proved)
тИ┤ тИЖDBC тЙЕ тИЖEBC (ASA axiom)
тИ┤ BD = CE