4.6. SSS Triangle Congruence http://www.ck12.org
EF=
√
( 5 − 4 )^2 +( 2 −(− 5 ))^2
=
√
( 1 )^2 +( 7 )^2
=
√
1 + 49
=
√
50 = 5
√
2
DF=
√
( 1 − 4 )^2 +(− 3 −(− 5 ))^2
=
√
(− 3 )^2 +( 2 )^2
=
√
9 + 4
=
√
13
We see thatAB=DE,BC=EF, andAC=DF. Recall that if two lengths are equal, then they are also congruent.
Therefore,AB∼=DE,BC∼=EF, andAC∼=DF. Because the corresponding sides are congruent, we can say that
4 ABC∼= 4 DEFby SSS.
Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter4SSSTriangleCongruenceB
Concept Problem Revisited
From what we have learned in this section, the two triangles are not congruent because the distance from the fridge
to the stove in your house is 4 feet and in your neighbor’s it is 4.5 ft. The SSS Postulate tells us that all three sides
have to be congruent.
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. TheSSS Triangle Congruence Postulatestates that if three sides in one
triangle are congruent to three sides in another triangle, then the triangles are congruent.
Guided Practice
- Determine if the two triangles are congruent.
- Fill in the blanks in the proof below.
Given:AB∼=DC,AC∼=DB
Prove: 4 ABC∼= 4 DCB