To check: Whether two isosceles
Answer to Problem 3WE
Two isosceles triangles are sometimes similar.
Explanation of Solution
Given information:
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.
A triangle in which two sides are equal is called as isosceles triangle.
Case 1:
Consider the following figures of two isosceles triangles:
Here, triangles ABC and PQR are isosceles as two sides in each of the triangles are equal.
Check whether the sides of triangles ABC and PQR are proportional.
So,
In this case, as the corresponding sides are not proportional, triangles ABC and PQR are not similar.
Case 2:
Consider the following figures:
Here, triangles ABC and PQR are isosceles as two sides in each of the triangles are equal.
And
In this case as the corresponding angles are equal and the corresponding sides are proportional, triangles ABC and PQR are similar.
From cases 1 and 2, it can be observed that two isosceles triangles may or not be similar that is two isosceles triangles are sometimes similar.
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