Question 147105: pleaseee help!
You have recently seen that there is no generally reliable SSA criterion for congruence. If the angle part of such a correspondence is a RIGHT angle, however, the criterion IS reliable. Justify this so-called hypotenuse-leg criterion (which is abbreviated HL.)
Answer by mangopeeler07(462)   (Show Source):
You can put this solution on YOUR website! First I'll assume that you are wondering what this means. That means that if two right triangles have congruent hypotenuses and a congruent pair of legs, then those triangles are congruent.
Next I'll assume that you are wondering why this is true for right triangles. This is true because all right triangles already have one angle in common. The right angle. So there is not that possible variation that there is for other triangles who have sides in common (as far as the angles go). Also this is true because of the Pythagorean theorem. If you assign a and b to legs and c to the hypotenuse,  will always equal  . Therefore, if two right triangles have the same a and c, they must also have the same b so that the equation will be true.
Lastly, I'll assume that you are wondering why this is not true for nonright triangles. It is because there is no angle in common necessarily. So two sides can be congruent but the triangles not be congruent because the third sides are not congruent. For example, you can have a triangle with the side lengths 3, 4, and 2. Then you can have a triangle with side lengths 3, 4, and 6. Even though two sides are in common, these triangles are not congruent because of their third sides.
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