Congruence criteria for right triangles

For right triangles fewer pieces of information are needed compared to the general case, because having a right angle is already one extra datum. Let us look at the specific criteria, which all descend from the three general criteria.

Theorem — Congruence of right triangles

Two right triangles are congruent if they have respectively congruent:

1. the two legs (from the first criterion — SAS);
2. hypotenuse and one leg (from the third criterion — SSS, the second leg is obtained by Pythagoras);
3. hypotenuse and one acute angle (from the second criterion — the second acute angle is the complementary one);
4. a leg and the adjacent acute angle (from the second criterion — ASA);
5. a leg and the opposite acute angle (from the second criterion — ASA, the other acute angle is the complementary one).

A right triangle: the two legs $a,b$, the hypotenuse $c$ and the two acute angles $\alpha,\beta$ (complementary).

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Topics: Euclidean geometry
Concepts: Congruence · Congruence criteria · Right triangle
Skills: Synthetic geometry · Reasoning by cases
People: Pythagoras