Which of the following is a false statement?
(a) If the areas of two similar triangles are equal then the triangles are
congruent.
(b) The ratio of the areas of two similar triangles is equal to the ratio
of their corresponding sides.
(c) The ratio of the areas of two similar triangles is equal to the ratio
of squares of their corresponding medians.
(d) The ratio of the areas of two similar triangles is equal to the ratio
of squares of their corresponding altitudes.
Answers
Given Statements
To Find : : false statement
(a) If the areas of two similar triangles are equal then the triangles are
congruent.
(b) The ratio of the areas of two similar triangles is equal to the ratio
of their corresponding sides.
(c) The ratio of the areas of two similar triangles is equal to the ratio
of squares of their corresponding medians.
(d) The ratio of the areas of two similar triangles is equal to the ratio
of squares of their corresponding altitudes.
Solution :
(a) If the areas of two similar triangles are equal then the triangles are
congruent. -TRUE ( as Ratio of area = Square of ratio of corresponding sides) as area is equal hence Ratio of area = 1 => atio of corresponding sides = 1 Hence triangles are
congruent
The ratio of the areas of two similar triangles is equal to the ratio
of their corresponding sides. - FALSE
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides
The ratio of the areas of two similar triangles is equal to the ratio
of squares of their corresponding medians. - TRUE
The ratio of the areas of two similar triangles is equal to the ratio
of squares of their corresponding altitudes. - TRUE
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