The correct option is Option C: the value of AE is 12 units.
What are congruent triangles?
Congruent triangles are the triangles whose size and shapes are the same. The angle and the sides of two congruent triangles are also congruent.
Here given in the question
CB = AB
∠DBC = 90°
∠ABE = ∠DBC = 90° (opposite angles formed by the intersection of AC and DE.)
As ∠CBE and ∠ABE are supplementary angles and form a straight line.
∠CBE + ∠ABE =180°
⇒∠CBE = 180° - ∠ABE = 180°- 90°= 90°
Between triangle Δ CBE & ΔABE
∠CBE = ∠ABE = 90°
CB = AB given
BE = BE common
triangle Δ CBE & ΔABE are congruent.
=> Δ CBE ≅ ΔABE( by S-A-S Congruency)
=> CE = AE ( as triangle Δ CBE & ΔABE are congruent then the sides are same.)
=> AE = 12 units
Therefore The correct option is Option C: the value of AE is 12 units.
Learn more about congruent triangles
here: https://brainly.com/question/1675117
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