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Prove the Triangle-Angle-Bisector Theorem. In the diagram given with the theorem, draw an auxiliary line \overrightarrow{BE} (in red) so that \overrightarrow{BE}||\overrightarrow{DA}. Extend \overrightarrow{CA} to meet\overrightarrow{BE} at point F. Given: \overrightarrow{AD} bisects \angle CAB. \frac{CD}{DB} = \frac{CA}{BA} Prove: Statements Reasons 1. \overrightarrow{AD} bisects \angle CAB. 1. Given 2. \angle 1 \cong \angle 2 2. Definition of an angle bisector \angle 1 \angle 2 \angle 3 \angle 4 E F 3 A 1 2 4 B D C

          Prove the Triangle-Angle-Bisector Theorem. In the diagram given with the
theorem, draw an auxiliary line \overrightarrow{BE} (in red) so that \overrightarrow{BE}||\overrightarrow{DA}. Extend \overrightarrow{CA} to meet\overrightarrow{BE} at point F.

Given: \overrightarrow{AD} bisects \angle CAB.
\frac{CD}{DB} = \frac{CA}{BA}
Prove:

Statements
Reasons
1. \overrightarrow{AD} bisects \angle CAB.
1. Given
2. \angle 1 \cong \angle 2
2. Definition of an angle bisector
\angle 1
\angle 2
\angle 3
\angle 4
E
F
3
A
1 2
4
B
D
C

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Prove the Triangle-Angle-Bisector Theorem. In the diagram given with the
theorem, draw an auxiliary line BE (in red) so that BE||DA. Extend CA to meetBE at point F.

Given: AD bisects ∠CAB.
(CD)/(DB) = (CA)/(BA)
Prove:

Statements
Reasons
1. AD bisects ∠CAB.
1. Given
2. ∠1 ≅∠2
2. Definition of an angle bisector
∠1
∠2
∠3
∠4
E
F
3
A
1 2
4
B
D
C

Added by John M.

Geometry A Common Core Curriculum

Ron Larson, Laurie Boswell 1st Edition

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Prove the Triangle-Angle-Bisector Theorem In the diagram given with the theorem, draw an auxiliary line BE (in red) so that BE intersects AD. Extend CA to meet BE at point F. Given: AD bisects angle CAB Prove: Statements: 1. AD bisects angle CAB 2. Line AD intersects line BE [Reasons: 1. Given 2. Definition of an angle bisector]

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