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2.(e) Give reasons for the following : 

(e)     Square is also a parallelogram.

 Square is also a parallelogram as its opposite sides are parallel.

2.(d)   Give reasons for the following : 

(d)     Squares, rectangles, parallelograms are all quadrilaterals. 

Squares, rectangles, parallelograms are all quadrilaterals as they all have four sides.

2.(c)     Give reasons for the following :

(c)     A square can be thought of as a special rhombus. 

A square can be thought of as a special rhombus because like a rhombus it has all sides equal but all its angles are also equal.

2.(b)     Give reasons for the following : 

 (b)     A rectangle can be thought of as a special parallelogram. 

 A rectangle can be thought of as a special parallelogram as it s a parallelogram only but with all angles equal to ninety degrees.

2.(a)  Give reasons for the following :

(a)     A square can be thought of as a special rectangle. 

A square can be thought of as a special rectangle as it is a rectangle only but with all sides equal.

1. 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.

(a) True. (b) True. (c) True. (d) True. (e) False. (f) False.

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

            

(a)(i) Acute angled triangle.     (ii) Isosceles triangle. (b)(i) Right angled triangle.     (ii) Scalane triangle. (c)(i) Obtuse angled triangle.     (ii) Isosceles triangle. (d)(i) Right angled triangle.     (ii) Isosceles triangle. (e)(i) Acute angled triangle.     (ii) Equilateral triangle. (f)(i) Obtuse angled triangle.    (ii) Scalane triangle.      

2. Match the following :         

Measure of triangles Types of triangle
(i) 3 sides of equal length (a) Scalene
(ii) 2 sides of equal length (b) Isoscles right angled 
(iii) All sides of different length (c) Obtuse angled
(iv) 3 acute angles (d) Right angled 
(v) 1 right angle (e) Equilateral
(vi) 1 obtuse angle (f) Acute angled
(vii) 1 right angle with two sides of equal length (g) Isosceles

 

Measure of triangles Types of triangle (i) 3 sides of equal length (e)Equilateral (ii) 2 sides of equal length (g) Isoscles (iii) All sides of different length (a) Scalene (iv) 3 acute angles (f) Acute angled   (v) 1 right angle (d)Right angled (vi) 1 obtuse angle (c) Obtuse angled (vii) 1 right angle with two sides of equal length (b) Isoscles right angled

1.  Name the types of following triangles :

            (a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.

            (b) \Delta ABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.

            (c) \Delta PQR such that PQ = QR = PR = 5 cm.

            (d) \Delta DEF with m\angle D=90^{\circ}

            (e) \Delta XYZ with m\angle Y=90^{\circ} and XY = YZ.

            (f) \Delta LMN with m\angle L=30^{\circ}, m\angle M=70^{\circ} and m\angle N=80^{\circ}

(a) Scalane Triangle. (b) Scalane Triangle. (c) Equilateral Triangle. (d) Right angled Triangle. (e) Right angled isosceles Triangle. (f) Acute angled Triangle.

4. 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.

                

(a) CE = 5 - 3 = 2 units      EG = 7 - 5 = 2 units          Therefore CE = EG. (b) CE = EG therefore PE bisects CG. (c) PE is the perpendicular bisector for line segments DF and BH (d) (i) AC = 3 - 1 = 2 units          FG = 7 - 6 = 1 unit            Therefore AC > FG             True     (ii) CD = 4 - 3 = 1 unit          GH = 8 - 7 = 1 unit           Therefore CD = GH           True        ...

3. 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?

The angles of the two set quares are (i) 90o, 60o and 30o (ii) 90o, 45o and 45o Yes they have the common angle measure 90o

2.  Let \overline {PQ} be the perpendicular to the line segment \overline {XY} . Let \overline {PQ} and \overline {XY} intersect in the point A. What is the measure of \angle PAY ?

 PQ and XY intersect at A Therefore 

1.  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.

 (a) The adjacent edges of a table top are models for perpendicular lines. (b) The lines of a railway track are not models for perpendicular lines as they are parallel to each other. (c) The line segments forming the letter ‘L’ are models for perpendicular lines. (d) The line segments forming the letter ‘V’ are models for perpendicular lines.

11. Measure and classify each angle :

              

                    

ANGLE MEASURE TYPE
\angle AOB    
\angle AOC    
\angle BOC    
\angle DOC    
\angle DOA    
\angle DOB    

  

  ANGLE MEASURE TYPE 40o Acute Angle 125o Obtuse Angle 85o Acute Angle 95o Obtuse Angle 1400 Obtuse Angle 1800 Straight Angle   

9. Find the angle measure between the hands of the clock in each figure :

             

The angle measure between the hands of the clock in each figure is (a) 90o (b) 30o (c) 180o

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

             

(a) Measure of the given along = 40o  (b) Measure of the given along = 130o  (c) Measure of the given along = 65o  (d) Measure of the given along = 135o 

7.  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 _______.

(a) An angle whose measure is less than that of a right angle is acute. (b) An angle whose measure is greater than that of a right angle is obtuse. (c) An angle whose measure is the sum of the measures of two right angles is straight. (d) When the sum of the measures of two angles is that of a right angle, then each one of them is acute. (e) When the sum of the measures of two angles is that of...

6.  From these two angles which has larger measure? Estimate and then confirm by measuring them.

                  

By estimation followed by confirmation by measurement we know that the second angle is greater.

5. Which angle has a large measure? First estimate and then measure.

Measure of Angle A =                                                                                  

Measure of Angle B =                                                                                  

Measure of Angle A = 40o Measure of Angle B = 60o

4.Measure the angles given below using the Protractor and write down the measure.

        Measure the angles given below using the Protractor and write down the measure

(a) 45o (b) 125o (c) 90o (d) 60o, 90o and 125o
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