The hypotenuse and the right-angled side correspond to the coincidence of two right-angled triangles.

Prove the condition of two Rt△ congruences: one hypotenuse of two right-angled (Rt) triangles is equal to one right-angled side, then two right-angled (Rt) triangles are congruent, abbreviated as HL.

Remember: the premise is that it must be a right triangle (Rt). H is the abbreviation of (hypotenuse) and L is the abbreviation of (right angle).

Rt△ABC≌Rt△ACB(HL)

It is proved that a2+B2 = C2； can be obtained from Pythagorean theorem.

Because the right angle side c is always equal to the other side a.

So b= root sign (c 2-a 2)

Because the three sides are equal.

So according to SSS, it can be proved that two triangles are congruent.

Therefore, HL is established.

Extended data

HL theorem is a theorem to prove the congruence of two right triangles. It is proved that the hypotenuse and right-angled side of two right-angled triangles are equivalent. The judging theorem is that if the hypotenuses of two right-angled triangles and a right-angled side are equal, then the congruence of these two right-angled triangles (abbreviated as HL) is a special judging method, which can be transformed into SSS, which is the case that SAS can confirm.

Theorem content

Two right-angled triangles (Rt triangles) whose hypotenuse and a right-angled side correspond to the same congruence (abbreviated as "HL") are called "(right-angled) congruence triangles".

Congruent triangles is defined as

After rotation, translation and rotation, two triangles that can completely overlap are called congruent triangles, and the three sides and three angles of the two triangles are equal.

When two triangles completely overlap, the fixed points that overlap with each other are called corresponding vertices, the edges that overlap with each other are called corresponding edges, and the angles that overlap with each other are called corresponding angles. Besides HL, there are four ways to determine whether two triangles are congruent (where S is an edge and A is an angle):

1, SSS: congruence of three triangles with equal sides.

2.SAS (Corner Side): Two sides and their included angle correspond to the congruence of a triangle.

3.ASA (Angle and Angle): the combination of two angles and their corresponding equal triangle clamping edges.

4.AAS (corner edge): two corners and the opposite side of one corner correspond to equal triangular congruence.