Write a two-column proof. Given: bar(MN) ~= bar(MP), bar(NO) ~= bar(PO) Prove: /_N ~= /_P 12210203572.jpg

Step 1
Given:
${\displaystyle \overline{MN}\stackrel{\sim }{=}\overline{MP},\overline{NO}\stackrel{\sim }{=}\overline{PO}}$

To prove:
${\displaystyle \mathrm{\angle }N\stackrel{\sim }{=}\mathrm{\angle }P}$
Step 2
Thus, The reflexive property of congruence,
${\displaystyle \overline{MO}\stackrel{\sim }{=}\overline{MO}}$
Now Triangles are congruent if all three sides in one triangle are congruent to the corresponding sides in the other.
By SSS congruence,
${\displaystyle \mathrm{△}MNO\stackrel{\sim }{=}\mathrm{△}MPO}$
Corresponding parts of congruent triangle (CPCT).
Their corresponding sides are equal and angles are equal.
Therefore, ${\displaystyle \mathrm{\angle }N\stackrel{\sim }{=}\mathrm{\angle }P}$