Final answer:
To prove that triangle AEB is congruent to triangle CEB, one can use the properties of a rhombus and the SAS postulate to show that they have two sides and the included angle congruent.
Step-by-step explanation:
The student's question involves proving that triangle AEB is congruent to triangle CEB given that ABCD is a rhombus with AE congruent to EC. To prove this, we can use the properties of a rhombus and the concept of congruent triangles.
In a rhombus, all sides are of equal length, which means AB = BC = CD = DA. Also, the diagonals of a rhombus bisect each other at right angles. Given AE ≅ EC, we know that E is the midpoint of AC, implying AE = EC. Since ABCD is a rhombus, we also know that the diagonals bisect the angles, so ∠AEB is congruent to ∠CEB.
By the Side-Angle-Side (SAS) postulate, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. Since AE = EC, AB = BC, and ∠AEB ≅ ∠CEB, we can therefore conclude that triangle AEB is congruent to triangle CEB.