In the figure AD is a diameter of a circle with centre O. If AB||CD, prove that AB=CD
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According to the information provided, the figure formed is attached.
in triangles ABO and DOC,
BO = OD (Radius)
Ang. BOA = Ang. DOC (Vertically opp angle)
AO= OC (Radius)
By SAS, ABO is congruent to DOC.
By CPCT, AB = CD
in triangles ABO and DOC,
BO = OD (Radius)
Ang. BOA = Ang. DOC (Vertically opp angle)
AO= OC (Radius)
By SAS, ABO is congruent to DOC.
By CPCT, AB = CD
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Answer:
a.s.a.(cpctc)
Step-by-step explanation:
draw perpendicular joining midpoints of AD and CD
since AD is a transversal cutting through two parallel lines, angle BAD and angle CDA is equal (alternate interior angles).
since the hypotenuse for both triangles are the radius r=r
bisectors from center of circle to chords are perpendiculars so 90degree=90degree
A.S.A.
both triangles are congruent
since AE = E'D
BA = 2 AE = CD
=> AB=CD
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