Question 1
Given here are some figures.
(1) |
(2) |
(3) |
(4) |
(5) |
(6) |
(7) |
(8) |
Classify each of them on the basis of the following.
(a) Simple curve
(b) Simple closed curve
(c) Polygon
(d) Convex polygon
(e) Concave polygon
Question 2
What is the sum of the measures of the angels of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)
Question 3
How many diagonals does each of the following have?
(a) A convex quadrilateral
(b) A regular hexagon
(c) A triangle
Question 4
Explain why a rectangle is a convex quadrilateral.
Question 5
What is a regular polygon?
State the name of a regular polygon of
(i) 3 sides
(ii) 4 sides
(iii) 6 sides
Question 6
How many diagonals does each of the following have?
(a) A convex quadrilateral
(b) A regular hexagon
(c) A triangle
Question 7
What is the sum of the measures of the angels of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)
Question 8
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 × 180° = (4 − 2) × 180° |
3 × 180° = (5 − 2) × 180° |
4 × 180° = (6 − 2) × 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
Question 9
Find the angle measure x in the following figures.
(a) |
(b) |
(c) |
(d) |
Question 10
(a) find x + y + z
(b) find x + y + z + w
Question 11
The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral.
Question 12
Find x in the following figures.
(a) |
(b) |
Question 13
Find the measure of each exterior angle of a regular polygon of
(i) 9 sides
(ii) 15 sides
Question 14
How many sides does a regular polygon have if the measure of an exterior angle is 24°?
Question 15
How many sides does a regular polygon have if each of its interior angles is 165°?
Question 16
(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?
Question 17
(a) What is the minimum interior angle possible for a regular polygon?
(b) What is the maximum exterior angel possible for a regular polygon?
Question 18
Explain how this figure is a trapezium. Which of its two sides are parallel?
Question 19
Identify all the quadrilaterals that have
(a) four sides of equal length
(b) four right angles
Question 20
Given a parallelogram ABCD. Complete each statement along with the definition or property used.
(i) AD = …
(ii) ∠DCB = …
(iii) OC = …
(iv) m∠DAB + m∠CDA = …
Question 21
Can a quadrilateral ABCD be a parallelogram if
(i) ∠D + ∠B = 180°?
(ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?
(iii) ∠A = 70° and ∠C = 65°?
Question 22
Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.
Question 23
The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)
(i) |
(ii) |
Question 24
State whether True or False.
(a) All rectangles are squares.
(b) All rhombuses are parallelograms.
(c) All squares are rhombuses and also rectangles.
(d) All squares are not parallelograms.
(e) All kites are rhombuses.
(f) All rhombuses are kites.
(g) All parallelograms are trapeziums.
(h) All squares are trapeziums.
Question 25
Given a parallelogram ABCD. Complete each statement along with the definition or property used.
(i) AD = …
(ii) ∠DCB = …
(iii) OC = …
(iv) m∠DAB + m∠CDA = …
Question 26
Consider the following parallelograms. Find the values of the unknowns x, y, z.
(i) |
(ii) |
(iii) |
(iv) |
(v) |
Question 27
Can a quadrilateral ABCD be a parallelogram if
(i) ∠D + ∠B = 180°?
(ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?
(iii) ∠A = 70° and ∠C = 65°?
Question 28
Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.
Question 29
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.
Question 30
Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.
Question 31
The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.
Question 32
In the above figure both RISK and CLUE are parallelograms. Find the value of x.
Question 33
In the given figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110, then ∠PTQ is equal to
(A) 60 (B) 70
(C) 80 (D) 90
Question 34
Given a parallelogram ABCD. Complete each statement along with the definition or property used.
(i) AD = …
(ii) ∠DCB = …
(iii) OC = …
(iv) m∠DAB + m∠CDA = …
Question 35
The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)
(i) |
(ii) |
Question 36
Name the quadrilaterals whose diagonals.
(i) bisect each other
(ii) are perpendicular bisectors of each other
(iii) are equal
Question 37
State whether True or False.
(a) All rectangles are squares.
(b) All rhombuses are parallelograms.
(c) All squares are rhombuses and also rectangles.
(d) All squares are not parallelograms.
(e) All kites are rhombuses.
(f) All rhombuses are kites.
(g) All parallelograms are trapeziums.
(h) All squares are trapeziums.
Question 38
Name the quadrilaterals whose diagonals.
(i) bisect each other
(ii) are perpendicular bisectors of each other
(iii) are equal
Question 39
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).
Question 40
State whether True or False.
(a) All rectangles are squares.
(b) All rhombuses are parallelograms.
(c) All squares are rhombuses and also rectangles.
(d) All squares are not parallelograms.
(e) All kites are rhombuses.
(f) All rhombuses are kites.
(g) All parallelograms are trapeziums.
(h) All squares are trapeziums.
Question 41
Name the quadrilaterals whose diagonals.
(i) bisect each other
(ii) are perpendicular bisectors of each other
(iii) are equal
Question 42
Explain why a rectangle is a convex quadrilateral.
Question 43
Explain how a square is.
(i) a quadrilateral
(ii) a parallelogram
(iii) a rhombus
(iv) a rectangle
Question 44
State whether True or False.
(a) All rectangles are squares.
(b) All rhombuses are parallelograms.
(c) All squares are rhombuses and also rectangles.
(d) All squares are not parallelograms.
(e) All kites are rhombuses.
(f) All rhombuses are kites.
(g) All parallelograms are trapeziums.
(h) All squares are trapeziums.
Question 45
Name the quadrilaterals whose diagonals.
(i) bisect each other
(ii) are perpendicular bisectors of each other
(iii) are equal
Question 46
Show that the diagonals of a square are equal and bisect each other at right angles.
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