Question

Prove that the triangles are equal with only providing the reason when the statements are already given

Answer 1

Proved below

Explanation:

To Prove: Triangle AEB ≅ Triangle CEB.

Step 1

Statement: ABCD is a rhombus

Reason: Given.

Step 2

Statement: AC and BD bisects each other.

Reason: The diagonals of a rhombus bisects each other.

Step 3

Statement: AE ≅ EC

Reason: A segment bisector divides a segment into two congruent segments.

Step 4

Statement: AB ≅ BC

Reason: All sides of a rhombus are congruent.

Step 5

Statement: BE ≅ BE

Reason: Reflexive Property

Step 6

Statement: ∆ AEB ≅ ∆ CEB

Reason: SSS

The triangles are thus proved to be congruent.