Question

given: ( abcd ) is a rhombus.
prove: ( \triangle aeb cong \triangle ceb ).
step
statement
reason
1
( abcd ) is a rhombus
given
2
type of statement

3
( overline{ae} cong overline{ec} )
a segment bisector divides a segment into two congruent segments
4
( overline{ab} cong overline{bc} )
all sides of a rhombus are congruent
5
( overline{be} cong overline{be} )
reflexive property
6
( \triangle aeb cong \triangle ceb )
sss

Explanation:

Step1: State the property of rhombus diagonals

In a rhombus, the diagonals bisect each other. So, \(BE\) is the bisector of \(AC\).

Step2: Fill in the statement for step 2

Since \(BE\) is the bisector of \(AC\), the statement for step 2 is "\(\overline{BE}\) is the bisector of \(\overline{AC}\)"

Answer:

\(\overline{BE}\) is the bisector of \(\overline{AC}\)