The hypotenuse leg (HL) notion will be discussed in this article. It’s one of the triangle’s congruency postulates, alongside SAS, SSS, ASA, and AAS. Let’s dig more into the HL congruence theorem.

The distinction is that the other four proposals are all triangular in nature. Because the hypotenuse is unquestionably one of the right-angled triangle legs, the Hypotenuse Leg Theory holds for the best triangular only.

What is the HL congruence theorem, and how does it work?


The hypotenuse leg thesis is a criteria used to determine if a given set of right triangular is congruent.


According to the hypotenuse leg (HL) idea, a given collection of triangles complies if the hypotenuse and equivalent lengths of one leg are identical.


Unlike other congruency postulates such as SSS, SAS, ASA, and AAS, which analyze three quantities, hypotenuse leg (HL) theory only considers two sides of a right triangle.


The Hypotenuse Leg Theory is Proven


Triangular ABC and QPR are right triangular in the diagram above, with AD = RQ and AC = PQ.


According to Pythagorean Thesis,


PQ2 = RQ2 + RP2 and AC2 = AB2 + BC2


Because AC = PQ, there is an alternative to getting.


RQ2 + RP2 = AB2 + BC2


However, AD = RQ.


As a substitute.


RQ2 + BC2 = RQ2 + RP2 RQ2 + RP2 RQ2 + RP2 RQ2 + RP2


To get, collect terms that are similar to each other.


RP2 = BC2.


As a result, ABC QPR.


Exercising 1.


Verify that both QPR and PR are compliant if PR QS.




Because both triangles QPR and PRS have a 90-degree angle at point R, they are right triangular.




PS + PQ (Hypotenuse).


Public Relations = Public Relations (Common side).