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TIME REMAINING
24:25
Given: m AEB = 45°
ZAEC is a right angle.
Prove: E bisects ZAEC.
С
Proof
We are given that m2AEB = 45° and ZAEC is a right
angle. The measure of ZAEC is 90° by the definition of
a right angle. Applying the
gives mZAEB
+ m_BEC = MZAEC. Applying the substitution property
gives 45° + m2BEC = 90°. The subtraction property
can be used to find mZBEC = 45°, so
ZBEC ZAEB because they have the same measure.
Since EB divides ZAEC into two congruent angles, it is
the angle bisector.
B
E