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Complete the similarity statement for the two quadrilaterals given.

Enter your answer in the box.

quadrilateral FSHB∼quadrilateral

HELP PLEASE Complete the similarity statement for the two quadrilaterals given Enter your answer in the box quadrilateral FSHBquadrilateral class=

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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

∴ [tex]\frac{FS}{KT}=\frac{SH}{TW}=\frac{HB}{WJ}=\frac{BF}{JK}[/tex]

If the above condition satisfied then the quadrilateral are similar.

Let us find these ratios

[tex]\frac{FS}{KT}=\frac{28}{21}=1.333[/tex]

[tex]\frac{SH}{TW}=\frac{24}{18}=1.333[/tex]

[tex]\frac{HB}{WJ}=\frac{18}{13.5}1.333[/tex]

[tex]\frac{BF}{JK}=\frac{18}{13.5}1.333[/tex]

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:

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.

[tex]\angle F=\angle K[/tex] (Given)

[tex]\angle S=\angle T[/tex] (Given)  

[tex]\angle H=\angle W[/tex] (Given)

[tex]\angle B=\angle J[/tex] (Given)

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

[tex]\frac{FS}{KT}= \frac{SH}{TW}=\frac{HB}{WJ}=\frac{FB}{KJ}=\frac{4}{3}[/tex]

The corresponding sides are proportional.

Therefore quadrilateral FSHB∼quadrilateral KTWJ.

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