The diagram is not drawn to scale. $D$ lies on $AB$, $F$ lies on $AC$, and $E$ lies on \(B

Question

The diagram is not drawn to scale. $D$ lies on $AB$, $F$ lies on $AC$, and $E$ lies on $BC$. Also, $DF\parallel BC$ and $DE\parallel AC$. It is given that $\triangle DFE\cong\triangle CEF$ and $\triangle ADF\sim\triangle ABC$, with vertices in corresponding order. Given $\angle AFD=37^\circ$, $\angle FED=81^\circ$, $AD:DB=3:2$ and $EC=12\text{ cm}$, state the side of $\triangle CEF$ corresponding to $DF$, find $\angle FEC$, state the scale factor from $\triangle ADF$ to $\triangle ABC$, find $BE$. $A$ $B$ $C$ $D$ $E$ $F$ $12\text{ cm}$

Accepted Answer

(a) $CE$. (b) $62^\circ$. (c) $\frac53$. (d) $8$cm.

Corresponding sides and angles

Corresponding sides and angles

Solution:

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