Problem: Prove that 90 = 110

Problem: Prove that 90 = 110.

Demonstration:
Hypothesis:
^
1) Angle CBA = 90 degrees
^
2) Angle DAB = 110 degrees
3) Segment BC = Segment AD
4) O is the intersection of the two perpendiculars in their middle (mediator) of segments AB and CD.
5) My major is not graphic design :)

_____________-------| C
___________----------------| . |
D \ . . | . |
\ . | . |
\ .... | . |
\ .. | . |
\ ... | . |
\ ... | . |
\ ... | .. |
\ ... || .. |
\ .... | .. |
\ O |
\ . . .|. . . |
\ . . . | . . . |
\ . . . | . . . |
A \_________________|________________| B

^ ^
Consider the angles CBA and DAB
^ ^ ^
CBA = CBO + OBA
^ ^ ^
DAB = DAO + OAB

^ ^
Angles OBA and OAB are equal because the triangle AOB is isosceles (OA=OB).

Consider triangles AOD and BOC
They have: AD = BC by construction
OA = OB, O belongs to the mediator of AB
OD = OC, O belongs to the mediator of CD

Then triangles AOD and BOC are congruent, and the corresponding angles are equal and we have:
^ ^
CBO=DAO
Getting back to the equalities:
^ ^ ^ ^ ^ ^
CBA = CBO + OBA = DAO + OAB = DAB

90 = 110

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