• A point is an exact location which has no length, no width and no thickness. A point is represented by a dot and we name it by a capital letter, say A.

• A curve is the path traced by a point on a plane. A curve that does not cross itself is known as a simple curve and a curve whose end points do not meet is known as an open curve.

A line is a straight path traced by a point. A line has only length and has no breadth or thickness. It is represented by two capital letters, say A and B and is written as AB or BA. It may also by represented by a small letters, say m.

A part of a line with two end pointsis called a line segment. A line segment has a fixed length. A line segment AB is denoted by AB or BA.

To measure the length of a line segment ,we use a ruler. Centimetre(cm) and millimetre(mm) are the units in a ruler.Each centimetre is divided in 10 equal millimetres.

MEASUREMENT OF LINE SEGMENT :

A ray is a part of a line having one fixed point which extends endlessly only in one direction. The given figure represents a ray and is denoted by AB.

• The outer boundary of a solid object is called its surface.A curved surface is a surface which does not follow a straight path. Ex- surface of a ball

• A plane is a flat surface which extends indefinitely in all directions. A plane surface is generally denoted by a small letter. Ex- surface of a table top

• Any open or closed figure drawnin a plane is called a plane figure. It can have straight and curved edges.

• The points A,B,C and D lie on the same line and these are calledcollinear points.• The points P, Q, and R do not lie on the same line and these are called non collinear points.

POINTS IN A PLANE:

• When two lines have a common point, the lines are called intersecting lines.

• Three or more lines in a plane are said to beconcurrent if they all pass through the samepoint. This point is called the point ofconcurrence. In the given figure,point e is pointof concurrence. And the lines are called concurrent lines.If three or more lines do not pass through the same point, then the lines are called non-concurrent lines.

CONCURRENT LINES:

1.Through a given point, an unlimited number of lines can be drawn.2. Only one line can be drawn passing through two given points.3.Two lines will either be parallel or intersect each other at a point in a plane. The point at which two lines intersect each other is known as the point of intersection.

Properties of Points and Lines in a Plane:

A line that divides the line segment into two equal parts is called a bisector of the line segment. AB bisects PQ at F. PF = FQ

A line which bisects a line segment at an angle of 90⁰ is called the perpendicular bisector of a line segment.XY bisects AB at 90⁰ and AO = OB.

BISECTOR OF A LINE SEGMENT:

PERPENDICULAR BISECTOR OF A LINE SEGMENT:

An angle is a figure formed by two rays with a common initial point.The common initial point is called vertex of the angle.The rays forming the angles are called the arms or sides of the angle. We use ' 'to denote an angle. Two line segments with a common end point also form an angle at that point.Protractor is an instrument used for measurement and construction of angles. It has 180 equal parts and each part is equal to 1⁰

ANGLE:

1. The shaded portion within the two armsof an angle is called the interior of the angle.2.The portion of the plane which is outsidethe two arms of an angle is called the exterior of the angle.3.The part of the plane consisting of all points lying on the arms of an angle is called the boundary of the angle.4. The interior of an angle along with its boundary is called the angular region.

Interior and Exterior of an Angle:

The amount of rotation through which one of the arms of an angle is rotated about the vertex is called the magnitude of the angle.One complete rotation is divided into 360 equal parts, each part is called adegree i.e 1⁰.1 turn = 360⁰1⁰ = 60'1' = 60''

Magnitude of an Angle:

: An angle whose measure is greater than 0⁰ but lessthan 90⁰.

: An angle whosemeasure is exactly 90⁰.

: An angle whose measure is greater than 90⁰ but less than 180⁰.

: An angle whose measure is exactly 180⁰.: An angle whose measure is greater than 180⁰

but less than 360⁰.: An angle whose measure is exactly 360⁰.

Types Of Angles:• Acute angle

• Right angle

• Obtuse angle

• Straight angle• Reflex angle

• Complete angle

Two angles in a plane are said to be adjacent angles if they have a common vertex, a common armand both are on the opposite sidesof the common arm.

A pair of adjacent angles are said toform a linear pair if their exterior arms form a straight line.

Adjacent Angles:

Linear Pair :

Angles on one side of a straight line always add up to 180⁰.

In the given figure, all the angles have ths same vertex O. Theseangles are called angles at a point. Sum ofall angles at a point is always 360⁰.

Angles on One Side of a Straight Line:

Angles at a Point :

If the sum of the measures of two angles is 90⁰, then the angles are said to be complementary angles. Complementary angles need not be adjacent angles.

If the sum ofthe measures of two angles is 180⁰, thenthe angles are said to be suppplementary angles. Supplementary angles need not be adjacent angles.

Complementary Angles :

Supplementary Angles :

Two angles aresaid to be congruent, if their measuresare the same. A and B are congruent.

A ray which divides an angle into two equal parts is called the bisector of the angle. AOB = BOC, therefore OB is thebisector of AOC

Congruent Angles:

Bisector of an Angle:

When two lines intersect each other at apoint, they form four angles like b, m, a, n.The opposite angles a and b; m and n are vertically opposite angles.

When two straight lines intersect each other, then the vertically opposite angles are equal.The adjacent angles are supplementarywhen two straight lines intersect each other.

Vertically Opposite Angles :

Properties of vertically opposite angles:

Two lines in a plane whichdo not intersect even if produced indefinitelyin either direction are called parallel lines.They do not have any common point.

A transversal is a straight line which intersects two or more straightlines in a plane.

Parallel Lines:

Transversal:

A transversal makes eight angles. Special names given to these angles are as follows:

Angles marked 1, 2 , 7, 8 are exterior angles.These are on the exterior part of the parallel lines.

Angles marked 3 , 4 , 5, 6 are interior angles.These are on the interior part of the parallel lines.

1. Exterior angles:

2.Interior angles:

3.Corresponding angles:

4.Alternate angles:The two pairs 1, 3 and 2, 4 are interior alternate angles.The two pairs 5, 7 and 6, 8 are exterior alternate angles.These angle have opposite positions with respect to each of the parallel lines.

5. Co-interior angles:

1.Corresponding angles are equal .In the figure, 1= 5, 2 = 6, 4 = 8 and 3 = 72.Alternate interior angles are equal . In the figure, 3 = 5 and 4 = 6.3. Alternative exterior angles are equal.In the figure, 2 = 8 and 1 = 7 4. Co-interiorangles are supplementary.In the figure, 3 + 6 = 180⁰ and 4 + 5 = 180⁰

Properties of Angles Associated with Parallel Lines:

Conversely, if a line intersects two lines such that a pair of alternate angles are equal , a pair of corresponding angles are equal or the sum of the interior angles on the same side of the transversal is 180⁰, then the lines are parallel to each other.

For more reference refer following links:

https://youtu.be/DmNCW9sIq10https://youtu.be/6RMN5Pf1fHUhttps://youtu.be/c0RWBk6wonk

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