4.9. HL Triangle Congruence http://www.ck12.org
We already know one pair of legs is congruent and that they are right triangles. The additional piece of information
we need is that the two hypotenuses are congruent,U T∼=F G.
Watch this video for help with the Examples above.
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/52623CK-12 Foundation: Chapter4HLTriangleCongruenceB
Vocabulary
Two figures arecongruentif they have exactly the same size and shape. By definition, two triangles arecongruent
if the three corresponding angles and sides are congruent. The symbol∼=means congruent. There are shortcuts
for proving that triangles are congruent. TheHL Triangle Congruence Theoremstates that 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. Aright trianglehas exactly one right (90◦) angle. The two sides adjacent to the right angle are called
legsand the side opposite the right angle is called thehypotenuse. HL can only be used with right triangles.
Guided Practice
- Determine if the triangles are congruent. If they are, write the congruence statement and which congruence
postulate or theorem you used. - Fill in the blanks in the proof below.
Given:
SV⊥WU
Tis the midpoint ofSVandWU
Prove:W S∼=UV