Direct answer :
[tex]\color{plum}\boxed{\bold{\tt Statements :} } [/tex]
- segment AE and BD bisect each other.
- ∠BCA and ∠DCE are equal.
- Segment AC and segment CE are equal.
- Segment BC and segment CD are equal.
- △ACB≅△ECD
[tex]\color{plum}\boxed{\tt Reasons : }[/tex]
- Given.
- They are vertically opposite angles, so they are equal.
- The bisector BD divides segment AE into two equal parts which are Segment AC and segment CE.
- The bisector AE divides the segment BD into two equal parts which are segment BC and segment CD.
- △ACB≅△ECD under the SAS congruence criterion because two sides and one included angle is equal.
Steps to derive these statements and reasons :
Given :
- segment AE and segment BD bisect each other
Which means :
- ∠BCA and ∠DCE are equal because they are vertically opposite angles.
- Segment AC = segment CE because the bisector BD divides the segment AE into two equal parts which are segment AC and segment CE.
- segment BC and segment CD will be equal because bisector AE divides the segment BD into two equal parts which are segment BC and segment CD.
Since two sides and one included angle is equal △ACB≅△ECD under the SAS congruence criterion .
