To check: Whether two right
Answer to Problem 2WE
Two right 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.
Case 1:
Consider the following figures of two right triangles:
Here,
So, corresponding angles are equal.
Now check whether the sides are proportional.
In this case although corresponding angles are equal but as the corresponding sides are not proportional, triangles ABC and PQR are not similar.
Case 2:
Consider the following figures:
Here,
So, corresponding angles are equal.
Now check whether the sides are proportional.
In this case as the corresponding angles are equal and the corresponding sides areproportional, triangles ABC and PQR aresimilar.
From cases 1 and 2, it can be observed that two right triangles may or not be similar that is two right triangles are sometimes similar.
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