To check: Whether congruent polygons are also similar.
Answer to Problem 8CE
Yes, if two polygons are congruent then polygons are also similar.
Explanation of Solution
Given information: Two polygons are congruent
Two polygons are said to be congruent if the following conditions are satisfied:
- Corresponding sides of the polygons are equal
- Corresponding
angles of the polygons are equal.
Two polygons are said to be similar if the following conditions are satisfied:
- Corresponding sides of the polygons are proportional.
- Corresponding angles of the polygons are equal.
Condition 2 is same in both the cases.
We only need to verify condition 1
Now if two polygons are congruent.
It means that the corresponding sides are equal.
That is ratio of the corresponding sides of both the polygons is equal to 1.
(For example:
Consider two
Let
If two triangles are congruent, it means
These imply
This implies that corresponding sides of the polygons are proportional
So, it can be concluded that if two polygons are congruent then polygons are also similar.
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