In a trapezoid the lengths of bases are 11 and 18. the lengths of legs are 3 and 7. the extensions of the legs meet at some point. find the length of segments between this point and the vertices of the greater base.

Step-by-step explanation:

Consider trapezoid ABCD with bases BC=11 units and AD=18 units.  The lengths of legs are AB=7 units and CD=3 units. Point S is the point of intersection of the extensions of the legs AB and CD.

Let BS=x units and CS=y units.

Consider triangles BSC and ASD. By AAA theorem these triangles are similar (because ∠SAD≅∠SBC, ∠ADS≅∠BCS and ∠S is common).

Then

Therefore,

The lengths of segments between point S and the vertices of the greater base are

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step-by-step explanation:

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step-by-step explanation: