How you can prove that two triangles are congruent?

Answer 1

In order for 2 triangles to be congruent, it must be true that each pair of corresponding sides are congruent (equal in length) and each pair of corresponding angles are congruent (equal in size).

It is not necessary to prove that all three pairs of sides and all three pairs of angles are congruent. If you prove that all the sides are congruent, then the angles must be congruent, too. This is known as SSS, the side-side-side method of proving congruency.

There a four basic ways to prove congruency. They are:

1. SSS (side-side-side) Prove that all three pairs of sides are equal in length.

2. SAS (side-angle-side) Prove that two sides and the angle between them are equal.

3. ASA (angle-side-angle) Prove that two angles and the side between them are equal.

4. AAS (angle-angle-side) Prove that two angles and a side that is NOT between them are equal.

Note that you cannot prove that triangles are congruent with AAA or SSA.

Note: for right triangles we can use HL. This is a special method that just looks at the hypotenuse and the leg of one triangle and compares it to the hypotenuse of the other. However, if they are both right triangle, the angle between the hypotenuse and the leg is a right angle so this is really just a special case of AAS that we can only use for right triangles.