EasyMathematicsHigh School (9–10)GeometryNumerical

D is on AB and E is on AC. AD = 3.6 cm, DB = 2.4 cm, AE = 3 cm and EC = 2 cm. Is DE parallel to BC?

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

$D$ is on $AB$ and $E$ is on $AC$ . $AD = 3.6$ cm, $DB = 2.4$ cm, $AE = 3$ cm and $EC = 2$ cm. Is $DE$ parallel to $BC$ ?

Need a reminder? The key ideaShow

The converse. If $\dfrac{AD}{DB} = \dfrac{AE}{EC}$ , then $DE \parallel BC$ . To test, cross-multiply: $AD \times EC = DB \times AE$ . In a trapezium $ABCD$ with $AB \parallel DC$ and diagonals meeting at $O$ , $\dfrac{AO}{OC} = \dfrac{BO}{OD}$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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