Question : Which of the following is a true statement?
Option 1: Two similar triangles are always congruent.
Option 2: Two similar triangles have equal areas.
Option 3: Two triangles are similar if their corresponding sides are proportional.
Option 4: Two polygons are similar if their corresponding sides are proportional.
Correct Answer: Two triangles are similar if their corresponding sides are proportional.
Solution :
(i) Two similar triangles are always congruent.
This statement is false.
Similar triangles have the same shape, but they may not have the same size. So, they are not always congruent.
(ii) Two similar triangles have equal areas.
This statement is false.
Similar triangles may have different areas because they can be different sizes.
(iii) Two triangles are similar if their corresponding sides are proportional.
This statement is true.
By definition, two triangles are similar if their corresponding sides are proportional.
(iv) Two polygons are similar if their corresponding sides are proportional.
This statement is false.
Two polygons are similar if their corresponding angles are equal and their corresponding sides are proportional.
Hence, the correct answer is 'the two triangles are similar if their corresponding sides are proportional.'
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