1. ## Congruent Segments

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

2. 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:

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

Reflexive Property of Congruence:

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

Definition of Angle Bisector

$\displaystyle \angle MNQ \cong \angle PNQ$

AAS: (Angle-Angle-Side Congruency Theorem)

$\displaystyle \triangle MNQ \cong \triangle PNQ$

CPCTC (Corresponding Parts of Congruent Trinagles are Congruent)

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

3. ## ok....

Originally Posted by masters
Hello,

Given:

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

Reflexive Property of Congruence:

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

Definition of Angle Bisector

$\displaystyle \angle MNQ \cong \angle PNQ$

AAS: (Angle-Angle-Side Congruency Theorem)

$\displaystyle \triangle MNQ \cong \triangle PNQ$

CPCTC (Corresponding Parts of Congruent Trinagles are Congruent)

$\displaystyle \overline{MQ} \cong \overline{PQ}$
Wonderfully done!