# Congruent Segments

• Dec 11th 2008, 08:25 PM
magentarita
Congruent Segments
Given segment NQ bisects angle MNP and angle M is congruent to angle P, prove segment MQ is congruent to segment PQ.
• Dec 12th 2008, 04:15 AM
masters
Quote:

Originally Posted by magentarita
Given segment NQ bisects angle MNP and angle M is congruent to angle P, prove segment MQ is congruent to segment PQ.

Hello,

Given:

$\overline{NQ}$ bisects $\angle MNP$ and $\angle M \cong \angle P$

Reflexive Property of Congruence:

$\overline{NQ} \cong \overline {NQ}$

Definition of Angle Bisector

$\angle MNQ \cong \angle PNQ$

AAS: (Angle-Angle-Side Congruency Theorem)

$\triangle MNQ \cong \triangle PNQ$

CPCTC (Corresponding Parts of Congruent Trinagles are Congruent)

$\overline{MQ} \cong \overline{PQ}$
• Dec 12th 2008, 04:32 PM
magentarita
ok....
Quote:

Originally Posted by masters
Hello,

Given:

$\overline{NQ}$ bisects $\angle MNP$ and $\angle M \cong \angle P$

Reflexive Property of Congruence:

$\overline{NQ} \cong \overline {NQ}$

Definition of Angle Bisector

$\angle MNQ \cong \angle PNQ$

AAS: (Angle-Angle-Side Congruency Theorem)

$\triangle MNQ \cong \triangle PNQ$

CPCTC (Corresponding Parts of Congruent Trinagles are Congruent)

$\overline{MQ} \cong \overline{PQ}$

Wonderfully done!