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For numbers 4 and 5, use a two-column proof format to prove the perpendicular
bisector theorem in two parts using the following figure:
In a circle, a diameter bisects a chord and an arc with the same endpoints if and
only if it is perpendicular to the chord.
P
Z
H
M
Y
4. Proof of Part 1: Given that XY is a diameter of Op and XYL LM at Z. Show that
XY bisects LM and the minor arc LM.
Hint: To prove that XY bisects LM, show that LZ ZM. To prove that XY bisects
the minor arc LM, show that XL XM and LY= MY.
5. Proof of Part 2: Given that XY is a diameter of OP and XY bisects LM at Z and
the minor arc LM. Show that XYLM.
