40.35 Given, m AEB = 45°
LAEC is a night angle
Prove E bisects LAEC,
Proof
We are given that mzAEB = 45and ZAEC is a right
angle. The measure of ZAEC is 90° by the definition of
a right angle. Applying the
gives IZAEB
+ m2BEC = MZAEC. Applying the substitution property
gives 45° + m_BEÇ = 90°. The subtraction property
can be used to find mæBEC = 45°so
ZBEC ZAEB because they have the same measure
Since El divides ZAEC into two congruent angles, it is
the angle bisector