Prove Me Wrong
Purce
Bard
Performance Tasks Prove Me Wrene
Unit 2: Tools and Techniques of Measuremen
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 E on BC that lies on the angle bisector of ZCAB. How far is point E
from point BP Show all your work.
3
(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 E that is perpendicular to AC at point F and say, "That means that EB and EP
are congruent." Is your friend correct? You can use algebra or trigonometry to confirm
or disprove their statement.
440
(²).
B
PERFORIAA