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?
Option 1: Two triangles are said to be congruent if all three sides of both triangles are equal.
Option 2: Two triangles are said to be congruent if 2 angles and the included side of one triangle are equal to 2 angles and the included side of the other triangle.
Option 3: Two triangles are said to be congruent if 2 sides and the included angle of one triangle are equal to 2 sides and the included angle of the other triangle.
Option 4: Two triangles are said to be congruent if any pair of 2 angles and any 1 pair of sides of both triangles are equal.
Question : Three sides of two triangles are 4, 5, and 6 cm. Select the INCORRECT statement.
Option 1: The angle opposite to the greater side in those triangles will be greater.
Option 2: The area of the two triangles will be different.
Option 3: The two triangles are congruent.
Option 4: The two triangles are scalene triangles.
Question : Which of the following statements is FALSE?
Option 1: Two triangles are congruent if the size and shape of the triangles may or may not be equal.
Option 2: SAS and SSS are both conditions of congruency of triangles.
Option 3: If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, the triangles are congruent.
Option 4: If two triangles are congruent, one of them can be superimposed on the other triangle.
Question : If the areas of two similar triangles are in the ratio 196 : 625, what would be the ratio of the corresponding sides?
Option 1: 14 : 25
Option 2: 13 : 20
Option 3: 14 : 20
Option 4: 13 : 25
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