EDULABZ INTERNATIONAL SYMMETRY, REFLECTION AND ROTATION

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1 17 SMMETR, REFLETIN ND RTTIN 1. Which of the following figures has only one line of symmetry? (a) rectangle (b) paralleogram (c) n isosceles trapezium (d) circle ns. (c) n isosceles trapezium has only one line of symmetry. D 2. rhombus has : (a) one line of symmetry (b) two lines of symmetry (c) four lines of symmetry (d) no line of symmetry ns. (b) rhombus has two lines of symmetry. 3. Draw all possible lines of symmetry in each of the following figures and state the number of lines of symmetry in each case : EDULZ (i) (ii) (iii) l INTERNTINL (iv) (v) (vi) (vii) ISE Math lass VII 1 Question ank

2 ns. The lines of symmetry in each of the given figures are drawn as given below : l (i) (ii) m (iii) (v) ne line of symmetry l m Four lines of symmetry p n (iv) (vi) Two lines of symmetry EDULZ l ne line of symmetry (vii) 4. State which of the following figures possess at least one line of symmetry : (i) INTERNTINL (ii) (iii) (iv) (v) ns. Figures (ii), (iii)and (v) has at least one line of symmetry as shown in the figure : ISE Math lass VII 2 Question ank

3 (ii) (iii) (v) 5. State the type (s) of symmetry possessed by each of the following figures. Explain each type of symmetry for these figures : (i) (iv) D (ii) J I EDULZ D E G H INTERNTINL ISE Math lass VII 3 Question ank F (iii) (v) ns. (i) Linear Symmetry No Point Symmetry Point is the centre of symmetry. Rotational Symmetry Rotational symmetry of order 2 about the point. (ii) Linear Symmetry Two lines of symmetry (i) the line joining the points and F (ii) the line joining the mid-points of D and IH. Point Symmetry The point is the centre of symmetry. Rotational Symmetry Rotational symmetry of order 2 about the point. (iii) Linear Symmetry No Point Symmetry The point the centre of symmetry. Rotational Symmetry Rotational symmetry of order 2 about the point. (iv) Linear Symmetry Two lines of symmetry (i) the line joining the points and (ii) the line joining the points and D. Point Symmetry The point of intersection of the line and D is the centre of symmetry. Rotational Symmetry Rotational symmetry of order 2 about the point. Linear Symmetry No. (v) Point Symmetry No Rotational Symmetry Rotational symmetry of order 3 about the point.

4 6. In each figure, given below, find the image of the line sigment in the line PQ (i) P Q (ii) P Q ns. (i) P L M Q (ii) Steps of onstruction: (i) From and, Draw perpendiculars on PQ intersecting PQ at L and M. (ii) Produce L to such that L = L and produce L to such that L = L and Produce M to such that M = M, is the image of the line segment in PQ 7. Draw a regular octagon and draw all possible lines of symmetry in it. ns. In a regular octagon DEFGH, there can be eight lines of symmetry as shown. G EDULZ H F INTERNTINL 8. Draw all possible lines of symmetry in : (a) a regular pentagon (b) a regular hexagon (c) a regular hexagon ns. (a) In a regular pentagon, there are five lines of symmetry. E D P L M Q ISE Math lass VII 4 Question ank

5 (b) In a regular hexagon, there are six lines of symmetry. 9. onstruct a triangle having = 5 cm, = 90 and = 45. Draw all possible lines of symmetry. ns.steps of construction: (i) We draw a line segment = 5 cm. (ii) With as centre draw a ray making an angle of 90 and with making an angle of 45 meeting each other at. Thus, is the required triangle. (iii) Draw the bisector of which bisect the side. This is the only line of symmetry. 10. onstruct a square having each side equal to 4 cm. Draw all possible lines of symmetry. ns. Stemps of construction : (i) We draw a line segment = 4 cm (ii) With and as a centre draw perpendiculars and cut off = D = 4 cm (iii) Join D Thus, D is the required square. 4 cm D 4 cm (iv) Join and D. (v) Draw perpendicular bisectors of sides, D, D and. Hence, a square has four lines of symmetry cm onstruct an equilateral triangle with each side 6 cm. In the triangle draw, draw all the possible lines of symmetry. ns. Steps of onstruction : (i) We draw a line segment = 6 cm 6 cm 6 cm (ii) With and as a centre and radius 6 cm, draw two arcs intersecting each other at. 6 cm EDULZ INTERNTINL 5 cm 45 ISE Math lass VII 5 Question ank

6 (iii) Join and Thus, is required equilateral triangle. (iv) Draw the angle bisectors of, and. Thus, there are three lines of symmetry in an equilateral triangle. 12. onstruct a triangle PQR such that PQ = 4.2 cm, P = 75 and Q = 75. Draw its line (or lines) of symmetry). ns. We draw PQ = 4.2 cm P and Q draw a angles of 75 each so that P = 75 and Q = 75 and extend the rays to meet at R. PQR is the required triangle. PQR is isosceles as the sides opposite to equal angles are also equal. So, there is only one line of symmetry in an isosceles triangle onstruct a triangle such that = 5.2 cm P 4.2 cm Q = 4.3 cm and = 3.5 cm. Rotate the triangle through 60 (anticlockwise) about the point. re the two triangle congruent? ns. Draw a line segment = 5.2 cm with and as centre draw two arcs = 3.5 cm and = 4.3 cm to meet them at. Joint and. Then is the required triangle Rotate the triangle through 60 (anticlockwise) about the point. The new triangle is. EDULZ oth the s are congruent (S.S.S. theory of congruence). 14. Plot the points ( 3, 4) and (2, 5) on the graph paper. Reflect the line segment in the x-axis to. Write down the co-ordinates of and. re and equal? ns. ( 3, 4) and (2, 5) are the given points. (2, 5) Joint the line segment. ( 3, 4) INTERNTINL N reflecting the line segment in the x-axis to, the co-ordinates of the points and are ( 3, 4) and (2, 5) reprectively. Measure and. es they are equal. 15. The triangle whose vertices are (2, 3), (3, 4) and (0, 5) is reflected in the y-axis to the triangle. Write down the co-ordinates of the vertices of triangle. re the two triangles congruent? ns. Triangle whose veritces are (2, 3), (3, 4) and (0, 5) is reflected in the ISE Math lass VII 6 Question ank 3.5 cm R 5.2 cm 4.3 cm X X ( 3, 4) (2, 5)

7 y-axis to form triangle. whose vertices have the co-ordinates as ( 2, 3), ( 3, 4) and (0, 5). The triangles and are congruents (y SSS theorem) ( 3,4) X (0, 5) (0, 5) (3,4) X ( 2, 3) (2, 3) 16. point P (2, 6) is rotated about the origin through 180 to the point P. Write down the co-ordiantes of P graphically. ns. Point P (2, 6) is rotated about the origin through 180 to the point P such that P = P The co-ordinate of the point P are ( 2, 6) as shown in the graph. 17. The point P (3, 8) is reflected in origin to point Q. The Point Q is further reflected in x-axis to point R. Find : (i) the co-ordinates of Q (ii) the co-ordinates of R (iii) the image of P(3, 8) in y-axis. ns. (i) The image of the given point P (3, 8) when reflected in origin is Q whose coordinates will be ( 3, 8). EDULZ Q ( 3, 8) INTERNTINL P (2, 6) X X P ( 2, 6) X X R ( 3, 8) P (3, 8) (ii) The image of Q ( 3, 8) when reflected in x-axis is R whose co-ordinates will be ( 3, 8) ISE Math lass VII 7 Question ank

8 18. Each of the point (0, 7), (8, 1, 0), (0, 5), D ( 7, 0) and E (0, 0) are reflected in orgin to points,,, D and E respectively. Write the co-ordinates of each of the image points,,, D, and E. ns. The points (0, 7), (8, 0), (0, 5). D ( 7, 0) and E (0, 0) are reflected in origin. Thus the co-ordinates of their images will be (0, 7), ( 8, 0) (0, 5), D (7, 0) and E (0, 0) X D ( 7, 0) ( 8, 0) EDULZ (0, 7) (0, 5) D ( 7, 0) (7, 0) D E E (0, 0) (8, 0) (0, 5) (0, 7) 19. has its vertices at ( 1, 2), ( 2, 4) and ( 3, 5). Then figure is first reflected in y-axis and then the new figure obtained is reflected in x-axis. Draw the image-figures. ns. Here, ( 1, 2), ( 2, 4) and ( 3, 5) 7 6 ( 2, 4) ( 3, 5) 5 (3, 5) 4 3 ( 1, 2) 2 1 X X INTERNTINL X ISE Math lass VII 8 Question ank

9 Figure is reflected in y-axis then (1, 2), (2, 4) and (3,5) then figure is reflected in x-axis then (1, 2), (2, 4), (3, 5). 20. D is a quadrilateral with its vertices at (2, 3), (5, 3), ( 2, 6) and D ( 4, 2). This quadrilateral is rotated about the origin, through 90 anticlockwise. Find the co-ordinates of its vertices in the new Position. ns. (2, 3), (5, 3), ( 2, 6) and D ( 4, 2) are the vertices of quadrilateral D. Now quadrilateral D is rotated about the origin through 90 anticlockwise, then the new co-ordinates of quadrilateral D are (3, 2) ( 3, 5) ( 6, 2) and D (2, 4). 21. PQRS is a quadrilateral with its vertices at P (3, 4) Q ( 3, 4) R ( 5, 2) and S (5, 3). This quadrilateral is rotated about the origin through 90 clockwise. Find the co-ordinates of its vertices in the new position. ns. P (3, 4) Q ( 3, 4) R ( 5, 2) and S (5, 3) are the vertices of a quadrilateral PQRS. Now quadrilateral PQRS is rotated about the origin through 90 clockwise then the new co-ordinates of quadrilateral P Q R S are P (4, 3), Q (4, 3), R ( 2, 5) and S ( 3, 5). 22. Plot the points (2, 3) ( 1, 2) and (0, 2) on the graph paper. Reflect the triangle in the x-axis to the triangle. Write down the co-ordinates of the vertices of. re the two triangles congruent? ns. Plot the point (2, 3), ( 1, 2) and (0, 2) on the graph paper. EDULZ X INTERNTINL ( 1, 2) ISE Math lass VII 9 Question ank (0, 2) (2, 3) ((2, 3) Draw the reflection (images), and of the points, and respectively in the x-axis. The triangle formed by joining the points, and is the required,. The co-ordinates of the vertices are (2, 3) ( 1, 2) and (0, 2). Measure the sides of the and. The two triangles and are congruent. X

10 23. Plot the points (3, 4) and (2, 5) on the graph paper. Rotate the triangle through 180 about (orgin). Find the co-ordinates of the vertices of this new triangle. ns. Plot the points (3, 4) and (2, 5) on the graph paper. ( 3, 4) (2, 5) X ( 2, 5) (3, 4) EDULZ Draw = 180 and = 180 such that = and =. Join The has been rotated through 180 about the origin and the triangle formed is. The co-ordinates of the points, and are (0, 0), ( 3, 4) and ( 2, 5) respectively. INTERNTINL X ISE Math lass VII 10 Question ank

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