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Match the following and give two new examples of each shape.

Solution: (a) Traffic cone and Waffle cone are examples of cone (b) Moonand Sun are examples of sphere (c) Gas cylinder and Candle... View Article

A diagonal is a line segment that joins any two vertices of the polygon and is not a side of the polygon. Draw a rough sketch of a pentagon and draw its diagonals.

Solution From the figure we may find AC, AD, BD, BE and CE are the diagonals... View Article

Draw a rough sketch of a regular octagon. (Use squared paper if you wish). Draw a rectangle by joining exactly four of the vertices of the octagon.

Solution The below figure is a regular octagon in which a rectangle is drawn by joining four of the vertices of the octagon.... View Article

Draw a rough sketch of a regular hexagon. Connecting any three of its vertices, draw a triangle. Identify the type of the triangle you have drawn.

Solution We can draw an isosceles triangle by joining three of vertices of a hexagon as shown in below figure... View Article

Name each polygon and make two more examples of each of these.

Solution (a) It is a closed figure and is made of four line segments. Hence, the given figure is a quadrilateral. Two more examples are (b) The... View Article

Examine whether the following are polygons. If any one among them is not, say why?

Solution: (i) The figure given above is not a closed figure. Hence, it is not a polygon. (ii) The figure given above is a polygon... View Article

A figure is said to be regular if its sides are equal in length and angles are equal in measure. Can you identify the regular quadrilateral?

Solution: Square is a regular quadrilateral because all the interior angles are of 900 and all sides are of same length.... View Article

Give reasons for the following: (a) A square can be thought of as a special rectangle.(b) A rectangle can be thought of as a special parallelogram.(c) A square can be thought of as a special rhombus. (d) Squares, rectangles, parallelograms are all quadrilaterals.(e) Square is also a parallelogram.

Solution: (a)A rectangle in which all the interior angles are of same measure i.e 900 and only opposite sides of the rectangle are of same... View Article

Say True or False: (a) Each angle of a rectangle is a right angle. (b) The opposite sides of a rectangle are equal in length. (c) The diagonals of a square are perpendicular to one another. (d) All the sides of a rhombus are of equal length. (e) All the sides of a parallelogram are of equal length. (f) The opposite sides of a trapezium are parallel.

Solution: (a) The given statement is True. Each angle of a rectangle is a right angle (b) The given statement is True. The... View Article

Try to construct triangles using match sticks. Some are shown here. Can you make a triangle with (a) 3 matchsticks? (b) 4 matchsticks? (c) 5 matchsticks? (d) 6 matchsticks? (Remember you have to use all the available matchsticks in each case) Name the type of triangle in each case. If you cannot make a triangle, think of reasons for it

Solution: (a)By using three match sticks we can construct a triangle as shown below The triangle shown above is an equilateral triangle (b) By... View Article

Name each of the following triangles in two different ways: (you may judge the nature of the angle by observation)

Solution: (i)The given figure represents Acute angled and isosceles triangle (ii)The given figure represents Right angled and scalene... View Article

Name the types of following triangles: (a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm. (b) ∆ABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm. (c) ∆PQR such that PQ = QR = PR = 5 cm. (d) ∆DEF with ∠D = 90° (e) ∆XYZ with ∠Y = 90° and XY = YZ. (f) ∆LMN with ∠L = 30°, ∠M = 70° and ∠N = 80°

Solution (a) Scalene triangle (b) Scalene triangle (c) Equilateral triangle (d) Right angled triangle (e) Right angled isosceles triangle (f)... View Article

Study the diagram. The line l is perpendicular to line m (a) Is CE = EG? (b) Does PE bisect CG? (c) Identify any two line segments for which PE is the perpendicular bisector. (d) Are these true? (i) AC > FG (ii) CD = GH (iii) BC < EH.

Solution: (a) Yes, since, CE = 2 units and EG = 2 units respectively (b) Yes. Since, CE = EG as both are of 2 units. Hence PE bisect CG... View Article

There are two set squares in your box. What are the measures of the angles that are formed at their corners? Do they have any angle measure that is common?

Solution The measure of angles in one set square are 300, 600 and 900 The other set square has a measure of angles 450, 450 and 900... View Article

Let [latex]overline{PQ}[/latex] be the perpendicular to the line segment [latex]overline{XY}[/latex] . Let[latex]overline{PQ}[/latex]and[latex]overline{XY}[/latex] intersect in the point A. What is the measure of ∠PAY?

Solution From the figure we note that the measure of ∠PAY is 900... View Article

Which of the following are models for perpendicular lines: (a) The adjacent edges of a table top. (b) The lines of a railway track. (c) The line segments forming the letter ‘L’. (d) The letter V.

Solution (a) The adjacent edges of a table top are perpendicular to each other. (b) The lines of a railway track are parallel to each other. (c)... View Article

Measure and classify each angle.

Measure and classify each angle: Angle Measure Type ∠AOB ∠AOC ∠BOC ∠DOC ∠DOA ∠DOB Solution:... View Article

Investigate In the given figure, the angle measure 300. Look at the same figure through a magnifying glass. Does the angle becomes larger? Does the size of the angle change?

Solution: The measure of an angle will not change by viewing through a magnifying glass... View Article

Find the measure of the angle shown in each figure. (First estimate with your eyes and then find the actual measure with a protractor).

Solution: The measures of the angles shown in above figure are 400, 1300, 650 and 1350... View Article

Fill in the blanks with acute, obtuse, right or straight: (a) An angle whose measure is less than that of a right angle is _ (b) An angle whose measure is greater than that of a right angle is (c) An angle whose measure is the sum of the measures of two right angles is _ (d) When the sum of the measures of two angles is that of a right angle, then each one of them is _ (e) When the sum of the measures of two angles is that of a straight angle and if one of them is acute then the other should be ____

Solution (a) An angle whose measure is less than that of a right angle is acute angle (b) An angle whose measure is greater than that of a... View Article

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