http://www.ck12.org Chapter 4. Triangles and Congruence
TABLE4.3:
Statement Reason
1.AB∼=DE
Cis the midpoint ofAEandDBGiven2.AC∼=CE,BC∼=CD Definition of a midpoint- 4 ACB∼= 4 ECD SSS Postulate
Make sure that you clearly state the three sets of congruent sides BEFORE stating that the triangles are congruent.
Prove Move:Feel free to mark the picture with the information you are given as well as information that you can
infer (vertical angles, information from parallel lines, midpoints, angle bisectors, right angles).
Example C
Find the distances of all the line segments from both triangles to see if the two triangles are congruent.
Begin with 4 ABCand its sides.
AB=
√
(− 6 −(− 2 ))^2 +( 5 − 10 )^2
=
√
(− 4 )^2 +(− 5 )^2
=
√
16 + 25
=
√
41
BC=
√
(− 2 −(− 3 ))^2 +( 10 − 3 )^2
=
√
( 1 )^2 +( 7 )^2
=
√
1 + 49
=
√
50 = 5
√
2
AC=
√
(− 6 −(− 3 ))^2 +( 5 − 3 )^2
=
√
(− 3 )^2 +( 2 )^2
=
√
9 + 4
=
√
13
Now, find the distances of all the sides in 4 DEF.