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Question

True or false? Justify your reasoning.

a. All isosceles triangles are congruent.

Solution

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Isosceles triangles are triangles with one pair of congruent sides. Consider the following examples ΔABC\Delta{ABC} and ΔDEF\Delta{DEF}:

'slader'

Note that both are isosceles triangles since both has one pair of congruent sides and yet ΔABC\Delta{ABC} is larger than ΔDEF\Delta{DEF}. Hence, all isosceles triangles are not necessarily congruent and the statement is false.

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