CK-12 Geometry - Second Edition

2.4. Algebraic and Congruence Properties http://www.ck12.org

Given:

−→

BFbisects^6 ABC;^6 ABD∼=^6 CBE

Prove:^6 DBF∼=^6 EBF

Solution:First, put the appropriate markings on the picture. Recall, that bisect means “to cut in half.” Therefore,
if

−→

BFbisects^6 ABC, thenm^6 ABF=m^6 F BC. Also, because the word “bisect” was used in the given, the definition
will probably be used in the proof.

TABLE2.17:

Statement Reason

1.

−→

BFbisects^6 ABC,^6 ABD∼=^6 CBE Given

2.m^6 ABF=m^6 F BC Definition of an Angle Bisector

3.m^6 ABD=m^6 CBE If angles are∼=, then their measures are equal.

4.m^6 ABF=m^6 ABD+m^6 DBF

m^6 F BC=m^6 EBF+m^6 CBE Angle Addition Postulate

5.m^6 ABD+m^6 DBF=m^6 EBF+m^6 CBE Substitution PoE

6.m^6 ABD+m^6 DBF=m^6 EBF+m^6 ABD Substitution PoE

7.m^6 DBF=m^6 EBF Subtraction PoE

8.^6 DBF∼=^6 EBF If measures are equal, the angles are∼=.

Prove Move:Use symbols and abbreviations for words within proofs. For example,∼=was used in place of the
wordcongruentabove. You could also use^6 for the wordangle.

Know What? RevisitedThe sisters, in order are: Sally, Sue, Sara. The sister on the left couldn’t have been Sara
because that sister lied. The middle one could not be Sara for the same reason. So, the sister on the right must be
Sara, which means she told Scott the truth and Sue is in the middle, leaving Sally to be the sister on the left.