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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 $\Delta{ABC}$ and $\Delta{DEF}$:

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

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