Final answer:
To prove triangles congruent, one may use postulates and theorems such as SAS, ASA, SSS, or the HL Congruence Theorem for right triangles, depending on the specific details provided about the triangles in question.
Step-by-step explanation:
The question asks about the postulates or theorems that can be used to prove triangles congruent. In geometry, proving two triangles are congruent means showing that they have exactly the same size and shape. This can be done using several different postulates and theorems, depending on the information provided about the triangles.
One of the most common methods is the Side-Angle-Side (SAS) Congruence Postulate, which states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. Another method is the Angle-Side-Angle (ASA) Congruence Theorem, which shows that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. The Side-Side-Side (SSS) Congruence Postulate demonstrates that if three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.
For right triangles, one might use the Hypotenuse-Leg (HL) Congruence Theorem, which states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, the triangles are congruent. This relates to the Pythagorean Theorem, which can sometimes be used to confirm whether a triangle is a right triangle based on the lengths of its sides.