Congruent Triangles - Hypotenuse and leg of a right triangle. (HL)
are congruent if the
hypotenuse and one corresponding leg are equal in both triangles.
There are five ways to test that two triangles are congruent. This is one of them (HL). For a list see
If, in two
and one leg are equal, then the triangles are congruent.
Drag any orange dot at P,Q,R. The other triangle LMN will change to remain congruent to the triangle PQR.
Notice that the the hypotenuse and leg are drawn in thick blue lines to indicate they
are the elements being used to test for congruence.
Notice that, since we know the hypotenuse and one other side, the third side is determined, due to
So this is really a version of the SSS case. (side-side-side).
What does this mean?
Because the triangles are congruent:
- The remaining third sides are equal (PQ=LM)
- The other two angles are equal (Q=M and R=N)
But don't forget:
Congruent triangles can be rotated and/or mirror images of each other (reflected).
(See Congruent triangles.)
In the figure on the right, the two triangles have all three corresponding sides equal in length
and so are still congruent, even though one is the mirror image of the other and rotated.
(C) 2009 Copyright Math Open Reference. All rights reserved