In the given figure below, AD/AE = AC/BD and . Show that BAE CAD .

Question

In the given figure below, AD/AE = AC/BD and $∠ 1 = ∠ 2 .$ . Show that Δ BAE $~$ ΔCAD .

Smart Achievers · Accepted Answer

In $∠ 1 = ∠ 2 .$

$∴$ AB = BD ..............(i)

Given, $\frac{A D}{A E} = \frac{A C}{B D}$

Using equation (i), we get $\frac{A D}{A E} = \frac{A C}{A B}$ .............(ii)

In ΔBAE and ΔCAD, by equation (ii), $\frac{A C}{A B} = \frac{A D}{A E}$

and $∠ A = ∠ A$ (common)

$∴$ ΔBAE $~$ ΔCAD [By SAS similarity criterion]

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