(i) Prove that each angle of a rectangle is 90°.
(ii) If the angle of a quadrilateral are equal, prove that it is a rectangle.
(iii) If the diagonals of a rhombus are equal, prove that it is a square.
(iv) Prove that every diagonal of a rhombus bisects the angles at the vertices.
Solution:
More Solutions:
- If the diagonal AC bisects A, then prove that:
- Prove that it is a square.
- Show that ABCD is a square.
- Show that PQ is bisected at O.
- Show that AC and PQ bisect each other.
- Prove that AP and DQ are perpendicular to each other.
- Prove that CQ || AP.
- The four bisectors form a quadrilateral ABCD.
- The bisector of ∠A meets DC in E and AB = 2 AD.
- A and B meet at E which lie on DC.