Olivia draws a regular pentagon and starts connecting its vertices to make a 5-pointed star. After drawing three of the lines in the star, she
becomes curious about two triangles that appear in the figure, A ABC and A CEB. They look similar to her. Prove that this is the case.
mzADB =
Thus, mZABC =
mzBEC =
, so mzDBA:
D
and mZBAC =
B
. Similarly, mzDCB =
C
because base angles of an isosceles triangle are congruent.
and mZACB=
Therefore, ABC and ABCE are similar.
So,