Not necessarily. Even if all three angles of one triangle are the same as the corresponding angles of the other, the triangles may be similar but not congruent.
And in this case, you don't even know that all three angles are the same.
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what is the congruent diagonals each of which divides the figure into two congruent isosceles right triangles
Similar, YES. Congruent, NO.
There are three basic types of triangles. Equilateral triangles have three congruent (equal) sides and three sixty-degree angles. Isosceles triangles have two congruent sides and the two angles opposite those sides are also congruent. Scalene triangles have no congruent sides or angles. Right triangles are another type of triangle and they have one ninety-degree angle. Right triangles can either be scalene or isosceles.
Absolutely. Any two congruent right triangles will form a rectangle, and if the right triangles are isosceles right triangles, they will form a square.
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