Question

in the diagram, ce=12 units and be=5 units. based on the given information, what is ae? 2 units 7 units 12 units 17 units

Explanation:

Step1: Identify the geometric property

From the diagram, we can see that \( AB = BC \) (marked with the same tick) and \( \angle ABE=\angle CBE = 90^\circ \) (right angle at \( B \)). Also, \( BE \) is a common side. So, triangles \( ABE \) and \( CBE \) are congruent by SAS (Side - Angle - Side) congruence criterion.

Step2: Use congruence to find \( AE \)

Since \( \triangle ABE\cong\triangle CBE \), their corresponding sides are equal. So, \( AE = CE \).
We know that \( CE = 12 \) units. So, \( AE=12 \) units.

Answer:

12 units (corresponding to the option "12 units")