Question

t is given that angle BAD = the angle CAE and angle B = angle D prove that AB/AD = AC/AE​

Answer 1

Step-by-step explanation:

angle BAD = angle CAE

angle BAD + angle CAD

= angle CAE + angle CAD.

angle BAC =angle DAE

angle B = angle D ( given )

then ∆BAC ~ ∆DAE ( AA SIMILARITY )

if triangles are similar , corresponding sides are proportional.

So , AB/AD = AC/AE.

Answer 2

In triangle ABC and triangle ADE,

ang.BAD+ang.DAC = ang.DAC+ang.CAE

=>ang.BAC = ang.DAE

ang.ABC=ang.ADE (Given)

Therefore, triangleABC is similar to triangleADE (A.A. similarity)

Therefore,

$\frac{ab}{ad} = \frac{ac}{ae}$

Hence, proved.