Which of the following statement is false?(a) All isosceles triangles are similar. (b) All quadrilateral are similar.(c) All circles are similar. (d) None of the above
Question
Which of the following statement is false?(a) All isosceles triangles are similar. (b) All quadrilateral are similar.(c) All circles are similar. (d) None of the above
Solution 1
To determine which statement is false, let's analyze each option:
(a) All isosceles triangles are similar: This statement is true. Isosceles triangles have two equal sides and two equal angles, which means they have the same shape and are therefore similar.
(b) All quadrilaterals are similar: This statement is false. Quadrilaterals can have different shapes and sizes, so not all quadrilaterals are similar.
(c) All circles are similar: This statement is true. Circles are defined by their radius and center, and any two circles with the same ratio of radii are considered similar.
(d) None of the above: This statement is not a specific statement but rather a negation of the previous options. Since option (b) is false, we can conclude that the correct answer is (b) All quadrilaterals are similar.
Therefore, the false statement is (b) All quadrilaterals are similar.
Solution 2
To determine which statement is false, let's analyze each option:
(a) All isosceles triangles are similar: This statement is true. Isosceles triangles have two equal sides and two equal angles, which means they have the same shape and are therefore similar.
(b) All quadrilaterals are similar: This statement is false. Quadrilaterals can have different shapes and sizes, so not all quadrilaterals are similar.
(c) All circles are similar: This statement is true. Circles are defined by their radius and center, and any two circles with the same ratio of radius to center distance are similar.
(d) None of the above: This statement is not a specific statement, but rather a negation of the previous options. Since option (b) is false, we can conclude that option (d) is the false statement.
Therefore, the false statement is (d) None of the above.
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