Congruent Triangles: Hypotenuse Leg Theorem

This video continues with the idea of congruent triangles by looking at the Hypotenuse Leg Theorem. If two triangles are each right triangles and contain a 90 degree angle and the hypotenuse and one of the legs in each triangle are equal, then the two triangles are congruent.

This theorem can be proven from the fact that the two triangles are right triangles and therefore the Pythagorean Theorem can be used to determine the 3rd side of each triangle and show that they must be equal. Once the third side of each triangle is known, then the side side side congruence postulate can be used to prove that the two triangles are in fact congruent.

Congruent triangles have both the same shape and the same size. Starting with some triangle, if it is translated (moved around), rotated, or reflected over some line, then the resulting triangle would retain the same shape and same size and thus would be congruent.

If a triangle is scaled or resized, then the two triangles would no longer be congruent. Triangles that have the same shape and all equal angles but do not have the same size are known as similar triangles.

Khan Academy exercises to practice:
1. Determine Congruent Triangles: https://www.khanacademy.org/math/geom...

2. Prove Triangle Congruence: https://www.khanacademy.org/math/geom...

3. Find Angles in Congruent Triangles: https://www.khanacademy.org/math/geom...

EulersAcademy.org