Question

In the figure AD is a diameter of a circle with centre O. If AB||CD, prove that AB=CD

Answer 1

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

Answer 2

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