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.
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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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Question : What is the ASA congruence rule of triangles, where A and S represent the angle and side of the triangle respectively?
Question : Three sides of two triangles are 4, 5, and 6 cm. Select the INCORRECT statement.
Question : Which of the following statements is FALSE?
Question : If the areas of two similar triangles are in the ratio 196 : 625, what would be the ratio of the corresponding sides?
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