Properties of Rhombus:
- The diagonals in a rhombus bisect each other.
- Each diagonal of a rhombus divides it into two congruent triangles.
- Opposite angles of a rhombus are equal and the sum of any two adjacent angles is 180°.
- In a rhombus the diagonals bisect each other at right angles, that is, the diagonals are perpendicular to each other and bisect each other.
- A quadrilateral is a rhombus, if and only if it has four congruent sides.
AB @ BC @ CD @ DA
- A parallelogram is a rhombus, if and only if its diagonals are perpendicular
- A parallelogram is a rhombus, if and only if each diagonal bisects a pair of opposite angles.
Directions: Read the above review points carefully and answer the following questions:
- Explain the different theorems of a rhombus, in your own words, with examples.
- Illustrate each of the above review points by drawing different rhombus.
- If one of the angles of a rhombus is 2 times the adjacent angle, then what will be the value of the angle opposite to it? Give reasons.
- A side of a rhombus is given by 16 cm. What will be the value of half of the other side? Give reasons.
- Question: The diagonals of rhombus ABCD intersect at O. Given that measure of ÐBAC is 530 and DO = 8, Find the mÐABO, mÐABC, mÐBCO, mÐBCD, mÐCDO, mÐCDA, mÐAOB, mÐBOC, mÐAOD, AO, AC, BD
(Hint: Use pythagorean theorem to find the measures of angles)