Question

Prove that: (i) A diagonal of a square makes an angle of 45 degree with the side of square. (ii) The diagonals of a rhombus are at right angles. (iii) A diagonal of a rhombus bisects the angles at vertices

Answer 1

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Step-by-step explanation:

1. It is one of the properties of a square that each diagonal bisects the angles at the two vertices through which they pass. Since each angle of the angles of a square is 90 degrees, each diagonal makes 45 degrees with side of a diagonal.

2. In any rhombus, the diagonals (lines linking opposite corners) bisect each other at right angles (90°). That is, each diagonal cuts the other into two equal parts, and the angle where they cross is always 90 degrees.

3. A quadrilateral is a rhombus if: it is a parallelogram, and a pair of adjacent sides are equal, its diagonals bisect each other at right angles, its diagonals bisect each vertex angle.