Question

Draw two congruent figures. Are they similar? Explain.

Answer 1

Hint: Start by drawing two congruent triangles. Now use the property of the congruent triangles that their corresponding angles are equal and using the AAA criteria show that they are similar as well.

Complete step-by-step answer:
Let us start by drawing the diagram for a better visualisation of the situation given in the question.

It is assumed that $\Delta ABC\text{ and }\Delta DEF$ are congruent. . Therefore, all three sides of $\Delta ABC$ are equal to corresponding sides of $\Delta DEF$ , we can say that the ratio of corresponding sides of the triangle are in the ratio of 1.
Also, as the triangle $\Delta ABC\text{ and }\Delta DEF$ are congruent, by using CPCT (corresponding part of congruent triangles), we can say that the corresponding angles of the congruent triangles are also equal. This can be represented as:
\[\begin{align}
  & \angle ABC=\angle DEF \\
 & \angle CAB=\angle FDE \\
 & \angle BCA=\angle EFD \\
\end{align}\]
So, using the AAA criteria we can say that the $\Delta ABC\text{ and }\Delta DEF$ are similar as well.
So, using the above result we can say that the congruent figures are similar as well.

Note: Remember that all congruent figures are similar, but all the similar figures are not necessarily congruent. Also, remember that in both cases, i.e., in case of similar as well as in case of congruent figures only the corresponding sides and angles are related to each other, there is no necessary relation between the non-corresponding sides or the angles.