Area of similar triangles are proportional to the squares of measures of their corresponding angles.Explain with reasons, whether the given statement are true or false.
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given statement is false .
explanation :- Area of similar triangles are proportional to the squares of their corresponding sides.
e.g., if ∆ABC and ∆DEF are similar
then, ar(∆ABC)/ar(∆DEF)=AB²/DE² = AC²/DF² = BC²/EF²
Since, the measure of corresponding angles of similar triangles are always equal.
∴ Area of similar triangles are not proportional to the squares of their corresponding angles.
Hence, the statement is false.
explanation :- Area of similar triangles are proportional to the squares of their corresponding sides.
e.g., if ∆ABC and ∆DEF are similar
then, ar(∆ABC)/ar(∆DEF)=AB²/DE² = AC²/DF² = BC²/EF²
Since, the measure of corresponding angles of similar triangles are always equal.
∴ Area of similar triangles are not proportional to the squares of their corresponding angles.
Hence, the statement is false.
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