Question

Please answer this question ​

Answer 1

Answer:

Given: In a ΔABC, ∠CAB = ∠CED

To Prove: AB × DC = ED × BC

Proof:

In ΔCAB and ΔCED

∵ ∠CAB = ∠CED (given)

∠C is common between both the triangles and hence equal

∴ ΔCAB ~ ΔCED    (Angle-Angle similarity criterion)

Therefore, the corresponding sides of ΔCAB and ΔCED will be proportional

Thus,

$\frac{BC}{DC}=\frac{AB}{ED}$

or, $AB\times DC=ED\times BC$             (Proved)

Hope the answer is helpful.