Your friend gives you the right triangle above and to the left and says. "Bisecting an angle is really easy. Take triangle ABC. If I wanted to bisect ZCAB, all I need to do is
find the midpoint of BC. The ray that goes from A through the midpoint of BC will
cut ZCAB in half, because it cuts the side BC in half Your friend then sketches the
triangle above and to the right.
(a) Convince your friend that they are wrong. Use what you know about trigonometry to
explain why ZCAD and ZDAB are not congruent.
(b) Locate the point Eon BC that lies on the angle bisector of ZCAB. How far is point E
from point B? Show all your work
(c) After you convince your friend that the bisector of ZCAB doesn't go through the
midpoint of BC, they say to you, "Now I remember! Every point on an angle bisector
is the same distance from the sides of the angle." They draw a line segment from
point that is perpendicular to AC at point F and say, "That means that EB and EF
are congruent." Is your friend correct? You can use algebra or trigonometry to confirm
or disprove their statement.
F
E
B
3