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Give reasons for the following:(a) A square can be through of as a special rectangle.(b) A rectangle can be through of as a special parallelogram.(c) A square can be through of as a special parallelogram.(d) Squares, rectangles, parallelograms are all quadrilaterals.(e) Square is also a parallelogram. |
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Answer» (a) A square can be through of as a special rectangle. In a rectangle all the interior angles are of the same measure i,e, 90° and the opposite side of the rectangle are of the same length where as in case of a square, all the interior angles are of 90° and all the sides are of the same length in other words, a rectangle with all sides equal becomes a square there, a square is a special rectangle. (b) A rectangle can be through of as a special parallelogram. Opposite sides of a parallelogram are parallel and equal in a rectangle, the opposite sides are parallel and equal also, all the interior angles of the rectangle are of the same Measure, i,e. 90°. in other words, a parallelogram with each angle a right angle becomes a rectangle Therefore a rectangle can be thought of as a specific parallelogram. (c) A square can be through of as a special parallelogram. All sides of a rhombus and a square are equal However, in case of a square, all interior angles are of 90° Measure. A rhombus with each angle a right angle becomes a square Therefore a square can be thought of as a special rhombus. (d) Squares, rectangles, parallelograms are all quadrilaterals. (e) Square is also a parallelogram. Opposite sides of a parallelogram are parallel and equal in a square, the opposite sides are parallel and the lengths of the four sides are equal Therefore a square can be thought 6 f as a special parallelogram. |
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