Answer:
See explanation
Step-by-step explanation:
Q11. Statement Reason
1. [tex]\overrightarrow {MO}[/tex] bisects [tex]\angle PMN[/tex] Given
2. [tex]\angle PMO\cong \angle NMO[/tex] Definition of angle bisector
3. [tex]\overline{MO}\cong \overline{MO}[/tex] Reflexive property
4. [tex]\overrightarrow {OM}[/tex] bisects [tex]\angle PON[/tex] Given
5. [tex]\angle POM\cong \angle NOM[/tex] Definition of angle bisector
6. [tex]\triangle PMO\cong \triangle NMO[/tex] ASA postulate
Q13.
1. Consider triangles ACB and DCE. In these triangles,
- [tex]\overline{BC}\cong \overline{EC}[/tex] - given;
- [tex]\overline{AC}\cong \overline{DC}[/tex] - given;
- [tex]\angle ACB\cong \angle DCE[/tex] - as vertical angles (by vertical angles theorem)
Hence, triangles ACB and DCE are congruent by SAS postulate.
2. congruent triangles have congruent corresponding sides, so
[tex]\overline{BA}\cong \overline{ED}[/tex]
