Question

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Answer 1

Answer:

Quadrilateral FSHB∼quadrilateral KTWJ.

Step-by-step 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

∴ $\frac{FS}{KT}=\frac{SH}{TW}=\frac{HB}{WJ}=\frac{BF}{JK}$

If the above condition satisfied then the quadrilateral are similar.

Let us find these ratios

$\frac{FS}{KT}=\frac{28}{21}=1.333$

$\frac{SH}{TW}=\frac{24}{18}=1.333$

$\frac{HB}{WJ}=\frac{18}{13.5}1.333$

$\frac{BF}{JK}=\frac{18}{13.5}1.333$

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

Answer:

The quadrilateral FSHB∼quadrilateral KTWJ.

Step-by-step 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.

$\frac{FS}{KT}= \frac{SH}{TW}=\frac{HB}{WJ}=\frac{FB}{KJ}=\frac{4}{3}$

The corresponding sides are proportional.

Therefore quadrilateral FSHB∼quadrilateral KTWJ.