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Understanding Quadrilaterals

Question

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Given a parallelogram ABCD. Complete each statement along with the definition or property used.

Solution

Some More Questions From Understanding Quadrilaterals Chapter

How many diagonals does each of the following have?

(a) A convex quadrilateral
(b) A regular hexagon
(c) A triangle

What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)

Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that).

Figure

Side

3

4

5

6

Angle sum

180°

2 x 180°

= (4 - 2) x 180°

3 x 180°

= (5 - 2) x 180°

4 x 180°

= (6 - 2) x 180°

What can you say about the angle sum of a convex polygon with number of sides?

(a) 7 (b) 8 (c) 10 (d) n

What is a regular polygon?
State the name of a regular polygon of

(i) 3 sides (ii) 4 sides (iii) 6 sides

Find the angle measure x in the following figures.

Find x in the following figures.

Find the measure of each exterior angle of a regular polygon of (i) 9 sides (ii) 15 sides

How many sides does a regular polygon have if the measure of an exterior angle is 24°?

How many sides does a regular polygon have if each of its interior angles is 165°?

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