(6) Given: \( N \) is the midpoint of \( \overline{M P}, Q \) is the midpoint of \( \overline{R P} \), and \( \overline{P Q} \cong \overline{N M} \).
Prove: \( \overline{P N} \cong \overline{Q R} \)
Hint: You will need the midpoint definition,

Answer

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Answer

Since \(\overline{PN} \cong \overline{QM}\), we have \(\overline{PN} \cong \overline{QR}\).

Steps

Step 1 ：Given \(N\) is midpoint of \(\overline{MP}\), by midpoint definition, \(\overline{MN} \cong \overline{NP}\).

Step 2 ：Given \(Q\) is midpoint of \(\overline{RP}\), by midpoint definition, \(\overline{RQ} \cong \overline{QP}\).

Step 3 ：Since \(\overline{PN} \cong \overline{QM}\), we have \(\overline{PN} \cong \overline{QR}\).