4.4. Congruence Statements http://www.ck12.org
We can also write this congruence statement several other ways, as long as the congruent angles match up. For
example, we can also write 4 ABC∼= 4 LMNas:
4 ACB∼= 4 LNM 4 BCA∼= 4 MNL
4 BAC∼= 4 MLN 4 CBA∼= 4 NML
4 CAB∼= 4 NLM
One congruence statement can always be written six ways. Any of the six ways above would be correct.
Example A
Write a congruence statement for the two triangles below.
To write the congruence statement, you need to line up the corresponding parts in the triangles:^6 R∼=^6 F,^6 S∼=^6 E,
and^6 T∼=^6 D. Therefore, the triangles are 4 RST∼= 4 F ED.
Example B
If 4 CAT∼= 4 DOG, what else do you know?
From this congruence statement, we can conclude three pairs of angles and three pairs of sides are congruent.
(^6) C∼= (^6) D (^6) A∼= (^6) O (^6) T∼= (^6) G
CA∼=DO AT∼=OG CT∼=DG
Example C
If 4 BU G∼= 4 ANT, what angle is congruent to^6 N?
Since the order of the letters in the congruence statement tells us which angles are congruent,^6 N∼=^6 Ubecause they
are each the second of the three letters.
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/52611