http://www.ck12.org Chapter 4. Triangles and Congruence
To determine if the triangles are congruent, each pair of corresponding sides and angles must be congruent.
Start with the sides and match up sides with the same number of tic marks. Using the tic marks:BC∼=MN,AB∼=
LM,AC∼=LN.
Next match the angles with the same markings;^6 A∼=^6 L,^6 B∼=^6 M, and^6 C∼=^6 N. Because all six parts are
congruent, the two triangles are congruent.
Example B
In order to say that 4 ABD∼= 4 ABC, you must determine that the three corresponding angles and sides are congruent.
Which pair of sides is congruent by the Reflexive Property?
The sideABis shared by both triangles. So, in a geometric proof,AB∼=ABby the Reflexive Property of Congruence.
Example C
If all three pairs of angles for two given triangles are congruent does that mean that the triangles are congruent?
Without knowing anything about the lengths of the sides you cannot tell whether or not two triangles are congruent.
The two triangles described abovemightbe congruent, but we would need more information to know for sure.
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/52607CK-12 Foundation: Chapter4CongruentTrianglesB