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3. Can a trapezium have all angles equal? Can it have all sides equal? Explain.

Trapezium has two sides parallel and other two sides are non parallel.Parallel sides may be equal or unequal but we cannot have a trapezium with all sides and angles equal.  

2. A square was defined as a rectangle with all sides equal. Can we define it as
rhombus with equal angles? Explore this idea.

Properties of rectangle are :  (1) All the properties of a parallelogram. (2) Each of the angles is a right angle. (3) Diagonals are equal. A square satisfies all the properties of rectangles so a square can be defined as a rectangle with all sides equal. Properties of rhombus are : (1) All the properties of a parallelogram. (2) Diagonals are perpendicular to each other. A square satisfies all...

1. A mason has made a concrete slab. He needs it to be rectangular. In what different ways can he make sure that it is rectangular?

(1).All the properties of a parallelogram. (2) Each of the angles is a right angle. (3) Diagonals are equal

6. ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you).

Draw line AD and DC such that  and .      and  ABCD is a rectangle as it has opposite sides equal and parallel. All angles of rectangle are  and rectangle has two diagonals equal and bisect each other. Hence, AO = BO = CO = DO  O is equidistant from A,B,C,D.  

5. Explain why a rectangle is a convex quadrilateral.

A rectangle is a convex quadrilateral because it has two diagonals and both lie in the interior of rectangle.

4. Name the quadrilaterals whose diagonals.

     (iii) are equal

The quadrilaterals whose diagonals are equal are square and rectangles.

4. Name the quadrilaterals whose diagonals.

    (ii) are perpendicular bisectors of each other

The quadrilaterals whose diagonals are perpendicular bisectors of each other are rhombus and square.

4. Name the quadrilaterals whose diagonals.

    (i) bisect each other

The quadrilaterals whose diagonals bisect each other are square,rectangle,parallelogram and rhombus.

3. Explain how a square is.

    (iv) a rectangle

A square is a rectangle sinse it has all interior angles of .

3. Explain how a square is.

    (iii) a rhombus

A square is a rhombus because square has four sides equal. 

3. Explain how a square is.

    (ii) a parallelogram

A square is a parallelogram because square has opposite sides parallel to each other.

3. Explain how a square is.

    (i) a quadrilateral

A square is a quadrilateral because square has four sides.

2. Identify all the quadrilaterals that have.

    (b) four right angles

All the quadrilaterals that have four right angles are rectangle and square

2. Identify all the quadrilaterals that have.

    (a) four sides of equal length

The quadrilateral having  four sides of equal length are square and rhombus.  

1. State whether True or False.

    (h) All squares are trapeziums.

True,All squares are trapeziums because all squares have pair of parallel sides.

1. State whether True or False.

    (g) All parallelograms are trapeziums.

True,all parallelograms are trapezium because they have a pair of parallel sides.

1. State whether True or False.

    (f) All rhombuses are kites.

True,all rhombuses are kites because they have two adjacent sides equal.  

1. State whether True or False.

    (e) All kites are rhombuses.

False, Kites do not have all sides equal so they are not rhombus.

1. State whether True or False. 

    (d) All squares are not parallelograms.

False. All squares have there opposite sides equal and parallel .Hence,they are parallelogram.

1. State whether True or False.

    (c) All squares are rhombuses and also rectangles.

True. All squares are rhombus because rhombus has opposite sides parallel and equal and same square has. Also all squares are rectangles because they have all interior angles as .  
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