Question

in triangle ABC if,angle 1 = angle 2 prove that AB/AC=BD/DC

Answer 1

Answer:

AB/AC = BD/DC

Step-by-step explanation:

in triangle ABC if,angle 1 = angle 2 prove that AB/AC=BD/DC

in Δ ABD using Sine Rule

AB/Sin∠D  = BD/Sin∠1   = AD/Sin∠B

=> AB/BD = Sin∠D/Sin∠1

in Δ ACD using Sine Rule

AC/Sin∠(180-D) = CD/Sin∠2   = AD/Sin∠C

=> AC/Sin∠D = CD/Sin∠2   = AD/Sin∠C

=> AC/CD = Sin∠D/Sin∠2

as ∠1 = ∠2 => Sin ∠1 = Sin∠2

=> AC/CD = Sin∠D/Sin∠1

=> AB/BD = AC/CD

=> AB/AC = BD/CD

=> AB/AC = BD/DC

QED

Proved

Answer 2

Answer:

Step-by-step explanation:

in triangle ABC if,angle 1 = angle 2 prove that AB/AC=BD/DC

in Δ ABD using Sine Rule

AB/Sin∠D  = BD/Sin∠1   = AD/Sin∠B

=> AB/BD = Sin∠D/Sin∠1

in Δ ACD using Sine Rule

AC/Sin∠(180-D) = CD/Sin∠2   = AD/Sin∠C

=> AC/Sin∠D = CD/Sin∠2   = AD/Sin∠C

=> AC/CD = Sin∠D/Sin∠2

as ∠1 = ∠2 => Sin ∠1 = Sin∠2

=> AC/CD = Sin∠D/Sin∠1

=> AB/BD = AC/CD

=> AB/AC = BD/CD

QED

Proved