# SCC Education

## Wednesday, 4 November 2015 1. How many diagonals does each of the following have?
(a) A convex quadrilateral (b) A regular hexagon (c) A triangle

2. What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex?  Using the formula: (n - 2)180°

3.What can you say about the angle sum of a convex polygon with number of sides?(a) 7 (b) 8 (c) 10

4. What is a regular polygon? State the name of a regular polygon of (i) 3 sides (ii) 4 sides (iii) 6 sides

5. Find the measure of each exterior angle of a regular polygon of (i) 9 sides (ii) 15 sides
8. How many sides does a regular polygon have if the measure of an exterior angle is 24°? Number of sides of a polygon =360/exterior angle
9. How many sides does a regular polygon have if each of its interior angles is 165°?  Exterior Angle = 180°-interior angle
10. (a) Is it possible to have a regular polygon with measure of each exterior angle as 22°?
(b) Can it be an interior angle of a regular polygon? Why?

[ If interior angle is 22° then the exterior angle  = 180°-22°=158°On dividing 360° by 158° we can’t get answer in whole number, so such a polygon is not possible.]

11. (a) What is the minimum interior angle possible for a regular polygon? Why?
(b) What is the maximum exterior angle possible for a regular polygon?
[Answer: The polygon with minimum number of sides is a triangle, and each angle of an equilateral triangle measures 60°, so 60° is the minimum value of the possible interior angle for a regular polygon. For an equilateral triangle the exterior angle is 180°-60°=120° and this is the maximum possible value of an exterior angle for a regular polygon.]

12. Can a quadrilateral ABCD be a parallelogram if
(i) <D + <B=180?    (ii) AB=DC= 8cm, AD= 4cm,and BC = 4.4 cm (iii) <A = 70 and <C = 65?
(i)It can be , but not always as you need to look for other criteria as well.
(ii) In a parallelogram opposite sides are always equal, here AD BC, so its not a parallelogram.
(iii) Here opposite angles are not equal, so it is not a parallelogram.

13. The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each of the angles of the parallelogram.
14. Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.

15. State whether True or False.
a) All rectangles are squares
Answer: All squares are rectangles but all rectangles can’t be squares, so this statement is false.
(b) All kites are rhombuses.
Answer: All rhombuses are kites but all kites can’t be rhombus
(c) All rhombuses are parallelograms
(d) All rhombuses are kites.
(e) All squares are rhombuses and also rectangles
Answer: True; squares fulfils all criteria of being a rectangle because all angles are right angle and opposite sides are equal. Similarly, they fulfil all criteria of a rhombus, as all sides are equal and their diagonals bisect each other.
(f) All parallelograms are trapeziums.
All trapeziums are parallelograms, but all parallelograms can’t be trapezoid.
(g) All squares are not parallelograms.
Answer: False; all squares are parallelograms
(h) All squares are trapeziums.
all four sides are equal then it

16.Identify all the quadrilaterals that have.
(a) four sides of equal length (b) four right angles
(a) If can be either a square or a rhombus.
(b) All four right angles make it either a rectangle or a square.

17.Explain how a square is.
(i) a quadrilateral (ii) a parallelogram (iii) a rhombus (iv) a rectangle
(ii) Opposite sides are parallel so it is a parallelogram
(iii) Diagonals bisect each other so it is a rhombus
(iv) Opposite sides are equal and angles are right angles so it is a rectangle.

18. Name the quadrilaterals whose diagonals.
(i) bisect each other (ii) are perpendicular bisectors of each other (iii) are equal
Answer: Rhombus; because, in a square or rectangle diagonals don’t intersect at right angles.

19 Explain why a rectangle is a convex quadrilateral.
Answer: Both diagonals lie in its interior, so it is a convex quadrilateral.

20 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.
Answer: If we extend BO to D, we get a rectangle ABCD. Now AC and BD are diagonals of the rectangle. In a rectangle diagonals are equal and bisect each other.
So, AC = BD , AO = OC ,BO = OD, And AO = OC = BO = OD So, it is clear that O is equidistant from A, B and C. 