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AD and BC are equal perpendicular to line segment AB show that CD bisects AB?
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AD and BC are equal perpendicular to line segment AB show that CD bise...



Proof:

Given:
- AD = BC
- AD ⊥ AB
- BC ⊥ AB

Proof:

1. Let's denote the point of intersection of CD and AB as E:
- Since CD is perpendicular to AB, angles CDE and CEA are right angles.

2. Triangles CDE and CEA are congruent:
- CD = BC (Given)
- CE = CE (Common side)
- Angle CDE = Angle CEA = 90° (Given)
- Therefore, by Side-Angle-Side postulate, triangles CDE and CEA are congruent.

3. By congruence, corresponding parts are equal:
- DE = EA

4. Therefore, CD bisects AB:
- By the Converse of the Midpoint Theorem, since DE = EA, CD bisects AB.
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AD and BC are equal perpendicular to line segment AB show that CD bisects AB?
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