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Any Point Equidistant from the End Points of a Segment Lies on the Perpendicular Bisector of the Segment

Question 3AD ...

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Question 3
AD and BC are equal perpendiculars to a line segment AB.
Show that CD bisects AB.

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Solution

$I n Δ B O C a n d Δ A O D ∠ B O C = ∠ A O D (v e r t i c a l l y o p p o s i t e a n g l e s) ∠ C B O = ∠ D A O (e a c h 90^{\circ}) B C = A D (g i v e n) ∴ Δ B O C ≅ Δ A O D (A A S c o n g r u e n c e r u l e) ∴ B O = A O (b y C P C T) \Rightarrow C D b i s e c t s A B$

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Any Point Equidistant from the End Points of a Segment Lies on the Perpendicular Bisector of the Segment

Standard IX Mathematics

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