Symmetry / Reflection

• A plane figure is symmetrical about a line if it is divided into two identical (coincident) parts by that line. The line is called its line (or axis) of symmetry.
• A plane figure is symmetrical about a point if every line segment joining two points of the figure and passing through the point is bisected at that point. The point is called its point (or center) of symmetry.
• A plane figure has a rotational symmetry if on rotation through some angle ( 180°) about a point it looks the same as it did in its starting position.
• If A° ( 180°) is the smallest angle through which a figure can be rotated and still looks the same, then it has a rotational symmetry of order 360/A.
• The reflection (or image) of a point P in a line AB is a point P' such that AB is the perpendicular bisector of the line segment PP'.
  To find the reflection (or image) of a point P in a line ABFrom P, draw PM perpendicular to AB and produce PM to P' such that MP'= MP, then P' is the reflection (or image) of P in the line AB.
• The reflection of the point P (x, y) in the x-axis is the point P'(x, -y).
• The reflection of the point P (x, y) in the y-axis is the point P'(-x, y).
• If a point P (x, y) is rotated through 180° (clockwise or anti-clockwise) about the origin to the point P', then co-ordinates of P' are (-x,-y).
• If a point P (x, y) is rotated through 90° clockwise about the origin to the point P', then co-ordinates of P' are (y,-x).
• If a point P (x, y) is rotated through 90° anti-clockwise about the origin to the point P', then co-ordinates of P' are (-y,x).

RIDDLE

Brain Teaser

CIRCLES

• A circle is the set of all those points, say P, in a plane, each of which is at a constant distance from a fixed point in that plane.
  The fixed point is called the center and the constant distance is called the radius.
  All radii of a circle are equal.

• A line segment joining any two points of a circle is called a chord of the circle.
  A chord of a circle passing through its center is called a diameter of the circle

• Length of diameter = 2 × radius

Exercise.
1. Fill in the blanks with correct word(s) to make the statement true:

(i) Radius of a circle is one-half of its.....

(ii) A radius of a circle is a line segment with one end point at..... and the other end on.....

(iii) A chord of a circle is a line segment with its end points....

(iv) A diameter of a circle is a chord that..... the center of the circle.

(v) All radii of a circle are.....

2. State which of the following statements are true and which are false:

(i) A line segment with its end-points lying on a circle is called a diameter of the circle.

(ii) Diameter is the longest chord of the circle.

(iii) The end-points of a diameter of a circle divide the circle into two parts; each part is called a semi-circle.

(iv) A diameter of a circle divides the circular region into two parts; each part is called a semi-circular region.

(v) The diameters of a circle are concurrent. The center of the circle is the point common to all diameters.

(vi) Every circle has unique center and it lies inside the circle.

(vii) Every circle has unique diameter.

Maths Challenge 2

7th July- 17th July

Each letter stands for a digit from 0 to 9. No two digits have the same letter code and each letter corresponds to a distinct digit. Discover the code so that the problems become true.

1. T H R E E + T H R E E + F O U R = E L E V E N

2. A B C D E x 4 = E D C B A

3. WRONG + WRONG = R I G H T