http://www.ck12.org Chapter 4. Triangles and Congruence
of arighttriangle are congruent to two sides of anotherrighttriangle, you can conclude that third sides are also
congruent.
HL Triangle Congruence Theorem:If the hypotenuse and leg in one right triangle are congruent to the hypotenuse
and leg in another right triangle, then the two triangles are congruent.
The markings in the picture are enough to say 4 ABC∼= 4 XY Z.
Notice that this theorem is only used with a hypotenuse and a leg. If you know that the two legs of a right triangle
are congruent to two legs of another triangle, the two triangles would be congruent by SAS, because the right angle
would be between them.
Example A
What information would you need to prove that these two triangles are congruent using the HL Theorem?
For HL, you need the hypotenuses to be congruent. So,AC∼=MN.
Example B
Determine if the triangles are congruent. If they are, write the congruence statement and which congruence postulate
or theorem you used.
We know the two triangles are right triangles. The have one pair of legs that is congruent and their hypotenuses are
congruent. This means that 4 ABC∼= 4 RQPby HL.
Example C
Determine the additional piece of information needed to show the two triangles are congruent by HL.