Question

in the adjoining figure AB and CD are equal chords. AD and BC intersect at E. prove that AE is equal to CE and BE is equal to DE.

Answer 1

Given:
AB and CD are equal chords
AD and CB intersect at point E
Prove:
AE is equal to CE
BE equal to DE
Proof:
AB = CD(opposite sides)
<B = <D (opposite angles)
<E = <E (common angle)
hence proved
AE = CE and BE = DE 
  (by CPCT )

Answer 2

Answer:

Given: AB = CD, AD and BC intersect at E

To prove: AE = DE, and BE = CE.

Construction: Join AC and BD.

Proof: In triangle AEB and triangle DEC,

          AB = CD (Given)

          angle BAD = angle DCB (angles in same segment)

          angle ABC = angle CDA (angles in same segment)

          triangle AEB = triangle DEC

          AE = DE, and BE = CE (corresponding parts of congurent triangle)

hence proved, hope you'll find this answer helpful

thank you:)))