In the diagram, CE = 12 and BE = 5. based on the given information, AE = ?

Solution:

We know that

∠ABE = ∠DBC = 90° (opposite angles)

Here,

∠CBA = 180° ( straight line)

Substituting the values

∠CBE = ∠CBA - ∠ABE = 180° - 90° = 90°

In triangle CBE and ABE,

∠CBE = ∠ABE = 90°

Given, CB = AB

And BE = EB ( common)

Therefore, Triangle CBE ⩬ triangle ABE by SAS criterion.

Thus, CE = AE by cpct

⇒ AE = 12 unit

Therefore, the value of AE is 12 units.

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In the diagram, CE = 12 and BE = 5. based on the given information, AE = ?

Summary:

In the diagram, CE = 12 and BE = 5. based on the given information, AE = 12 units.