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Not necessarily. You find the area of a triangle with the formula 1/2*base*height=Area.

Imagine two triangles, one with 3 inches for both the base and height, and one with 4.5 inches for the height and 2 inches for the base. Both of these triangles will have 9 sq. in. for their areas, but they are not congruent.

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Q: Are two triangles congruent if they have same area?
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