In the triangle AED and ABC, angles C and D are straight lines. Prove that these triangles are equal. If CO = OD.

Triangles AOC and BOD are rectangular, for which, by condition, OC = OD. Angle AOC = BOD as vertical angles. Then the right-angled triangles AOB and BOD are equal in leg and acute angle, which means AO = BO, AC = BD.

In right-angled triangles ABD and ABC, the hypotenuse AB is common, then the right-angled triangles ABD and ABD are equal in leg and hypotenuse, which was required to be proved.

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