Day 6
Right Triangle Congruence
Click here for the Intermath Definition of a right triangle.
Investigation: Draw two triangles that are congruent by SAS. Then draw two right triangles that are congruent by SAS. If you take out the A for angle, you are left with SS. In a right triangle, this is the same as LL, and since all right angles are congruent, LL for right triangles is actually the same as SAS for any triangle.
Try the same for HA, LA, and HL.
The theorems and postulate below are just extensions of previous theorems or postulates, such as AAS or SAS (See Day 2 in this Instructional Unit).. This is because all right triangles have one angle that is congruent, the right angle. Thus, you only need two other parts to prove two right triangles congruent.
Leg Leg Theorem (LL): If the legs of one right triangle are congruent to the corresponding legs of another triangle, then the triangles are congruent.
Hypotenuse Angle Theorem (HA): If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then the two triangles are congruent.
Leg Angle Theorem (LA): If one leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent.
Hypotenuse Leg Postulate (HL): If the hypotenuse and a leg on one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.