HardMathematicsHigh School (9–10)GeneralGeometry › TrianglesNumerical

ABCD is a trapezium with AB parallel to DC…

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

$ABCD$ is a trapezium with $AB$ parallel to $DC$ . Its diagonals meet at $O$ . $AO = 6$ cm, $OC = 15$ cm and $DO = 20$ cm. Find $\dfrac{AO}{OC}$ and $BO$ .

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.

← All Problems

← D and E are the midpoints of AB and AC in a triangle with AB = 14 cm, AC = 18 cm and BC = 16 cm…Next →

More onGeometry › Triangles

Discussion (0)

Loading…