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Choose whether the given statement is true or false.

The side opposite to the equal angles of a triangle may be unequal.

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True

False

answer is B.

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Detailed Solution

Consider a triangle XYZ with equal angles

∠ X Y Z = ∠ Y Z X

as,

Draw a bisector XM of

∠ Y X Z

, it meets YZ at M. Consider the triangles as XMY and XMZ, and the angles as

∠ X Y Z, ∠ Y Z X

.
Given that,

∠ X Y Z = ∠ Y Z X

… (1)
Since the common side is XM, then

X M = X M

… (2)
Now, since XM is bisector of

∠ Y X Z

, we can say that

∠ Y X M = ∠ Z X M

… (3)
By AAS criteria, from (1), (2), and (3), the triangles XMY and XMZ are congruent. The corresponding points must be equal

X Y = X Z

. So, the given statement is false.
Hence, the given statement is false.
The correct statement is: “The side opposite to the equal angles of a triangle may be equal.”

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