Question

If two sides of a cyclic-quadrilateral are parallel; prove that :

(i) its other two sides are equal.

(ii) its diagonals are equal.

Answer 1

(i) Given

Therefore (alternate angles)

Chord subtends on circumference.

Chord subtends on circumference.

Therefore (since equal chords subtend equal angles on the circumference)

(ii) Consider

is common

(proved above)

(angles in the same segment)

Therefore (by SAS axiom)

Therefore (corresponding parts of congruent triangles are equal)