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AD and BC are equal perpendicular to line segment AB show that CD bisects AB?
Most Upvoted Answer
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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AD and BC are equal perpendicular to line segment AB show that CD bisects AB? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about AD and BC are equal perpendicular to line segment AB show that CD bisects AB? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AD and BC are equal perpendicular to line segment AB show that CD bisects AB?.
AD and BC are equal perpendicular to line segment AB show that CD bisects AB? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about AD and BC are equal perpendicular to line segment AB show that CD bisects AB? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AD and BC are equal perpendicular to line segment AB show that CD bisects AB?.
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