Question

3. Read the section on How Can We Classify Special Quadrilaterals in a Hierarchy on pages 479.480. i. True or False: The categories for classifying quadrilaterals are mutually exclusive, i.e., a shape with 4 sides must be in exactly one category. ii. True or False: Suppose we have a list of 2 properties for a category, adding a third property to the list will add more shapes into the category. iii. True or False: All rectangles are parallelograms. iv. True or False: If a shape is a square then the shape is also a rectangle. v. True or False: If a shape is a rectangle then the shape is also a rhombus. vi. True or False: If a shape is a rhombus then the shape is also a parallelogram. vii. True or False: All quadrilaterals are rhombuses. viii. True or False: All parallelograms are trapezoids (defined as having at least one pair of parallel sides). ix. True or False: All parallelograms are trapezoids (defined as having exactly one pair of parallel sides).

Answer 1

Sno.	True/False	Remarks
i	FALSE	A quadrilateral is a polygon with four sides. But it is not compulsory a shape with 4 sides must be exactly in one category. For example A kite is a quadrilateral with exactly two pairs of adjacent congruent sides, A trapezoid is a quadrilateral with exactly one pair of parallel sides.
ii.	TRUE	For Example we have ,A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel
		A parallelogram also has the following properties:
		Opposite angles are congruent;
		Opposite sides are congruent;
		Adjacent angles are supplementary;
		The diagonals bisect each other.
		Upon adding the property of Diagonal intersection ar right angles become it an rhombus
		A rhombus is a parallelogram with four congruent sides. The plural of rhombus is rhombi
		A rhombus has all the properties of a parallelogram, plus the following:
		The diagonals intersect at right angles.
iii.	TRUE	A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals. On the other hand, not all quadrilaterals and parallelograms are rectangles.
iv.	TRUE	Every Square has all sides equal with right angle edges, Which completing the properties of rectangle
v.	FALSE	A rhombus has the diagonals intersect at right angles. But in the rectangle diagonal does not intersect at right angle
vi	TRUE	A rhombus is a parallelogram with four congruent sides.A rhombus has all the properties of a parallelogram, The diagonals intersect at right angles.
vii.	FALSE	All quadrilateral are not rombus but all the rombus are quadrilateral
viii.	FALSE	A trapezoid is a quadrilateral with exactly one pair of parallel sides
ix.	FALSE	A trapezoid is a quadrilateral with exactly one pair of parallel sides, but in the parallelogram have 2 pair of parallel sides