Answer:
See explanation
Step-by-step explanation:
Consider triangles ACM and BCM. In these triangles,
- [tex]m\angle 3=m\angle 4[/tex] - given;
- [tex]m\angle 1=m\angle 2=90^{\circ}[/tex] - definition of perpendicular lines CM and AB;
- [tex]\overline{CM}\cong \overline{CM}[/tex] - reflexive property.
So,
[tex]\triangle ACM\cong \triangle BCM[/tex] by ASA postulate (if one side and two angles adjacent to this side of one triangle are congruent to one side and two angles adjacent to this side of another triangle, then two triangles are congruent).
Two-column proof:
Statement Reason
1. [tex]m\angle 3=m\angle 4[/tex] Given
2. [tex]CM\perp AB[/tex] Given
3. [tex]m\angle 1=m\angle 2=90^{\circ}[/tex] Definition of perpendicular lines CM and AB
4. [tex]\overline{CM}\cong \overline{CM}[/tex] Reflexive property
5. [tex]\triangle ACM\cong \triangle BCM[/tex] ASA postulate
