Question

What are the differences between similar triangles and congruent triangles?

Answer 1

Hint: Here in this question we have been asked to write the differences between similar and congruent triangles. For answering this question we will define the terms congruent triangles and similar triangles first and then consider some examples and note down the differences.

Complete step-by-step solution:
Now considering from the question we have been asked to write the differences between similar and congruent triangles.
From the basic concepts of triangles we know that the two triangles are said to be congruent if they are of the same shape and size whereas two triangles are said to be similar if they are of the same shape but can be of different sizes.
Similar triangles have the same proportions.
The difference between congruence and similarity of triangles is that similar shapes can be resized versions of the same shape, whereas congruent figures have identical lengths.
Therefore we can conclude that a congruent triangle is a similar triangle whereas a similar triangle can be or cannot be congruent.
The differences can be listed out in tabular form as follows:

	Similar triangles	Congruent triangles
1	Triangles should have the same shape.	Triangles should have the same shape and size.
2	Triangles can have different sizes.	Triangles should have the same size.
3	Triangles have the same proportions.	Triangles are completely the same in all aspects.
4	They may or may not be congruent to each other.	They are also similar to each other.
5	They are resized versions of each other.	They are identical to each other.

Let us consider 3 triangles $\Delta ABC$ , $\Delta DEF$ and $\Delta GHI$ .

Here the triangle $\Delta ABC$ is identical to the triangle $\Delta DEF$ so they are congruent whereas both of them are resized versions of the triangle $\Delta GHI$ so they are similar to the triangle $\Delta GHI$.

Note: While answering questions of this type we should be sure with the concepts that we are using in the process. This is a purely concept based question. Similar triangles are of the same shape, that is they have all the three angles equal but the sides may or may not be equal whereas congruent triangles have both sides and angles equal.