Question

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Complete the similarity statement for the two quadrilaterals given.

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quadrilateral FSHB∼quadrilateral

Answer 1

Quadrilateral FSHB∼quadrilateral KTWJ.

Explanation:

Given two quadrilaterals we have to prove these two similar.

The two quadrilaterals are similar if the corresponding sides of these are proportional then only the quadrilateral are proportional i.e

∴
`(FS)/(KT)=(SH)/(TW)=(HB)/(WJ)=(BF)/(JK)`

If the above condition satisfied then the quadrilateral are similar.

Let us find these ratios

`(FS)/(KT)=(28)/(21)=1.333`

`(SH)/(TW)=(24)/(18)=1.333`

`(HB)/(WJ)=(18)/(13.5)1.333`

`(BF)/(JK)=(18)/(13.5)1.333`

All ratios are equal.

Hence, the corresponding sides and angles of these two quadrilaterals are proportional implies that these two are similar i.e quadrilateral FSHB∼quadrilateral KTWJ.

Answer 2

The quadrilateral FSHB∼quadrilateral KTWJ.

Explanation:

Two figures are congruent if their corresponding sides are proportional and the corresponding interior angles are congruent.

In quadrilateral FSHB and quadrilateral KTWJ.

`\angle F=\angle K` (Given)

`\angle S=\angle T` (Given)

`\angle H=\angle W` (Given)

`\angle B=\angle J` (Given)

All the corresponding interior angles are equal but the corresponding sides are not equal.

`(FS)/(KT)= (SH)/(TW)=(HB)/(WJ)=(FB)/(KJ)=(4)/(3)`

The corresponding sides are proportional.

Therefore quadrilateral FSHB∼quadrilateral KTWJ.