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    Exercise 8.3.4

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6th class > > Exercise 8.3.4

Exercise 8.3.4

1. State whether True or False

All rectangles are squares
All rhombuses are parallelograms
All squares are rhombuses and also rectangles
All squares are not parallelograms.
All kites are rhombuses.
All rhombuses are kites.
All parallelograms are trapeziums.
All squares are trapeziums.
True
False

2. Identify all the quadrilaterals that have.

(a) four sides of equal length: ,.

(b) four right angles:,.

3. Explain how a square is.

(i) a quadrilateral: because it has sides.

(ii) a parallelogram: because its opposite sides are and .

(iii) a rhombus: because all four sides are of length and its diagonals bisect each other at right angles.

(iv) a rectangle: because it has right angles and opposite sides that are equal and parallel.

4. Name the quadrilaterals whose diagonals.

(i) Diagonals bisect each other:

Parallelogram, , Rhombus, .

(ii) Diagonals are perpendicular bisectors of each other:

, Square.

(iii) Diagonals are equal:

Rectangle, .

5. Explain why a rectangle is a convex quadrilateral.

In Convex Quadrilaterals Diagonals lie in the interior.

Rectangle ABCD has Sides.Its diagonals AC and BD lie inside the rectangle.

Hence,ABCD is a convex Quadrilateral.

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).

ABCD is a rectangle as opposite sides are equal and parallel to each other and all the interior angles measure °.
Thus, AD ∥ BC, AB ∥ DC and AD = BC, AB = DC
In a rectangle, diagonals are of equal length and they bisect each other.
Hence, AO = OC = BO = OD
Therefore, O is equidistant from A, B, C, and D.

Try These

1.What is the sum of the measures of its exterior angles x, y, z, p, q, r?

x,y,z,p,q,r are all exterior angles.

Hence,x+y+z+p+q+r=degrees.

2. Is x = y = z = p = q = r? Why?

It is a hexagon with all sides .

a + r = a + x = a + y = a + z = a + p = a + q = degree.

Hence,x=y=z=p=q=r

3. What is the measure of each?

(i) exterior angle

All Interior angles are also equal.

Sum of all angles of hexagon is 720.

6a =720, a = 120.

Each exterior angle =r=x=y=z=p=q=180-a =

(ii) interior angle TO DO

4. Repeat this activity for the cases of (i) a regular octagon

Let interior angle be A.

8 * A = 1080

A=

All exterior angles be B.

B=180-135=.

(ii) a regular 20-gon

Let interior angle be A

20 * A = 3240

A = .

All exterior angles be B.

B=180-162=.

Try These

1.Take two identical set squares with angles 30° – 60° – 90° and place them adjacently to form a parallelogram as shown in Fig. Does this help you to verify the above property?

Property : The opposite sides of a parallelogram are of length.

As we can see in the figure above, the opposite sides of figure are equal.

The figure above is a rectangle which is part of parallelogram.