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G.SRT.4 WORKSHEET #1B
NAME: _______________________________
1
2. Prove the Angle Bisector Theorem.
The Angle Bisector Theorem states that an angle bisector of an angle of a triangle divides the opposite side in
two segments that are proportional to the other two sides of the triangle.
Given: ∆ABC where BD is an angle bisector.
Prove:
B
AB AD
=
BC DC
o
C
To get this proof moving I’m going to give you a little help – Create the
D
A
auxiliary line AE parallel to BD while also extending side CB until they
meet at point E.
o
E
B
o
o
C
D
A
HINT:
Have you seen this
relationship before?
E
B
C
A
D
G.SRT.4 WORKSHEET #1B
2
3. After figuring out the proof for the Angle Bisector Theorem a Kylie asks; “Could we have done the
auxiliary line parallel line to AB through D instead?” The teacher responds with “Great question Kylie, I’m
not sure but it looks like it should work because we make a ‘similar’ looking diagram”. See if Kylie is correct.
Given: ∆ABC where BD is an angle bisector.
Prove:
B
AB AD
=
BC DC
o
o
C
D
A
B
o
E
o
C
D
A
HINT:
Have you seen this
relationship before?
B
E
C
A
D
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