Question

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Answer 1

Given:

The figure of two quadrilaterals.

In $ABCD,AB=18,BC=20,CD=22,AD=24$

In $EFGH,EF=27,FG=30,GH=34, EH=36$

To find:

Whether the figures are congruent, similar or neither.

Solution:

Ratio of corresponding sides are:

$\dfrac{AB}{EF}=\dfrac{18}{27}$

$\dfrac{AB}{EF}=\dfrac{2}{3}$

Similarly,

$\dfrac{BC}{FG}=\dfrac{20}{30}$

$\dfrac{BC}{FG}=\dfrac{2}{3}$

$\dfrac{CD}{GH}=\dfrac{22}{34}$

$\dfrac{CD}{GH}=\dfrac{11}{17}$

And,

$\dfrac{AD}{EH}=\dfrac{24}{36}$

$\dfrac{AD}{EH}=\dfrac{2}{3}$

Clearly, $\dfrac{AB}{EF}=\dfrac{BC}{FG}=\dfrac{AD}{EH}\neq \dfrac{CD}{GH}$.

All corresponding sides are not proportional.

Therefore, the figures are neither similar nor congruent. Hence, third option is correct.