Chapter SR22, Problem 6P

Solution

Tell whether the figures are congruent, similar or neither. Explain.

Congruent.

Given:

The given figure.

  

Concept Used:

• Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
• If two figures or objects are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Calculation:

The given figure is −

  

In the given figures the two sides are parallel and two sides are non-parallel so the figures are parallelogram.

Ratio of corresponding sides −

  $\begin{array}{c}\frac{6}{3}=\frac{9}{4.5}=\frac{3}{1.5}=\frac{3}{1.5}\\ \frac{2}{1}=\frac{2}{1}=\frac{2}{1}=\frac{2}{1}\end{array}$

Ratio of corresponding sides are in equal proportion.

So corresponding sides are congruent.

And corresponding angles are also equal so angles are congruent.

Hence both the figures are congruent.