4.4. Congruence Statements http://www.ck12.org
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 more content.CK-12 Foundation: Chapter4CreatingCongruenceStatementsB
Concept Problem Revisited
If 4 ABC∼= 4 XY Z, thenBA∼=Y Xand^6 C∼=^6 Z.
Vocabulary
To becongruentmeans to be the same size and shape. Two triangles arecongruentif their corresponding angles
and sides are congruent. The symbol∼=meanscongruent.