4.3. Triangle Congruence using SSS and SAS http://www.ck12.org
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.
Example 6:Determine if the two triangles are congruent.
Solution:Use the distance formula to find all the lengths. Start with 4 ABC.
AB=
√
(− 2 −(− 8 ))^2 +(− 2 −(− 6 ))^2
=
√
( 6 )^2 +( 4 )^2
=
√
36 + 16
=
√
52 = 2
√
13
BC=
√
(− 8 −(− 6 ))^2 +(− 6 −(− 9 ))^2
=
√
(− 2 )^2 +( 3 )^2
=
√
4 + 9
=
√
13
AC=
√
(− 2 −(− 6 ))^2 +(− 2 −(− 9 ))^2
=
√
(− 4 )^2 +( 7 )^2
=
√
16 + 49
=
√
65
Now find the sides of 4 DEF.