In the figure given below, $A F, B E$ and $C D$ are parallel lines. Given that $A F = 7.5 c m, C D = 4.5 c m, E D = 3 c m, B E = x$ and $A E = y$ . Find the values of $x$ and $y$ .

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Solution

Triangles $A E F$ and $D E C$ are similar, so,
$\frac{A F}{C D} = \frac{A E}{E D} \Rightarrow y = \frac{7.5}{4.5} \times 3 = 5 c m$
Triangles $A E B$ and $A D C$ are similar, so
$\frac{A E}{A D} = \frac{B E}{C D} \Rightarrow x = \frac{5}{8} \times 4.5 = 2.8125 c m$

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In the figure below $A B$ , $C D$ and $E F$ are parallel lines. Given $A B = 7.5 c m$ , $D C = y c m$ . $E F = 4.5 c m$ , $B C = x c m$ and $C E = 3 c m$ . Calculate the values of $x$ and $y$ .

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In the given figure, $A B | | C D, A F | | E D, ∠ A F C = 68^{\circ}$ and $∠ F E D = 42^{\circ} .$ . Find $∠ E F D .$

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In the figure given below, AF,BE and CD are parallel lines. Given that AF=7.5cm,CD=4.5cm,ED=3cm,BE=x and AE=y. Find the values of x and y.

Triangles AEF and DEC are similar, so,AFCD=AEED⇒y=7.54.5×3=5cmTriangles AEB and ADC are similar, soAEAD=BECD⇒x=58×4.5=2.8125cm

In the figure given below, $A F, B E$ and $C D$ are parallel lines. Given that $A F = 7.5 c m, C D = 4.5 c m, E D = 3 c m, B E = x$ and $A E = y$ . Find the values of $x$ and $y$ .

Triangles $A E F$ and $D E C$ are similar, so,
$\frac{A F}{C D} = \frac{A E}{E D} \Rightarrow y = \frac{7.5}{4.5} \times 3 = 5 c m$
Triangles $A E B$ and $A D C$ are similar, so
$\frac{A E}{A D} = \frac{B E}{C D} \Rightarrow x = \frac{5}{8} \times 4.5 = 2.8125 c m$