In the diagram, CE=12 units and BE=5 units.

Line l is a perpendicular bisector of line segment A C. It intersects line segment A C at point B. Line l also contains points D and E. Line segments A B and B C are the same length.

Based on the given information, what is AE?

2 units
7 units
12 units
17 units

12 Units

Step-by-step explanation:

Step 1 :

Two triangles are said to be congruent if two sides of the triangles and the included angles are equal.

Step 2 :

Given  CE = 12 Units and BE = 5 units.

Line l is a perpendicular bisector of the line segment AC . So we have AB =  BC. (Given that line segments AB and BC are equal.

In triangle ABE, ∠ B is 90° [ Given that line l is perpendicular bisector of AC and B is the point of intersection]

In triangle CBE, ∠ B is 90° [ Given that line l is perpendicular bisector of AC and B is the point of intersection]

Step 3:

Triangles ABE and CBE are congruent.  [ As we have side AB = BC, side BE is common to both triangles and the included angle ABE and CBE of both the triangles are equal]

So as per the SAS [side angle Side] property of congruency of triangles, the triangles are equal.

This implies the 3rd side , AE is equal to CE.

Hence AE = CE = 12 units.

The right triangle

Step-by-step explanation: