Based on the information marked in the diagram, abc and def must be congruent. true or false?

All triangle congruence postulates are Side-Angle-Side, (SAS), Side-Side-Side (SSS), Angle-Angle-Side (AAS), Angle-Side-Angle (ASA), and hypotenuse leg theorem (HL).

Triangles are congruent by SAS when two sides and an included angle are congruent.
Triangles are congruent by SSS when all three sides are congruent.
Triangles are congruent by AAS when two consecutive angles and a side are congruent.
Triangles are congruent by ASA when two angles and an included side are congruent.
Triangles are congruent by HL when the hypotenuse and one leg of a right triangle are congruent.

If you look at this diagram, you see that two consecutive sides and one angle are marked as congruent. The postulate we have for two congruent sides and one congruent angle is SAS. However, the angle is not an included angle, thus they are not congruent by SAS. You might then say it is Side-Side-Angle congruence - but SSA is NOT a triangle congruence postulate.
Still, these are right triangles, and their hypotenuses and legs are marked as congruent, so they are congruent by HL.

The answer is A. True.

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