Geometry
Point
A fine dot on paper or a location on plane is called point. Point has no
length, breadth or thickness.
Line
A line is defined as a line of points that extends infinitely in both
directions.
P Q
Line Segment
A line segment is a part of line that is bounded by two distinct end
points and contains every point on the line between its end points.
A B
Ray
If a line segment is extended to unlimited length on one of the end
points, then it is called a ray.
A B
Important Points to be Remembered
(i) A line contains infinite points.
(ii) Infinite lines can pass through a point.
(iii) Two distinct lines in a plane cannot have more than one point common.
Angle
If two rays are drawn in different directions from y
a common initial point, then they are said to form Ra
an angle. Angle
O
(i) An angle of 90° is a right angle and an Ray
angle less than 90° is an acute angle.
(ii) An angle between 90° and 180° is an obtuse angle.
(iii) An angle between 180° and 360° is a reflex angle.
, (iv) The sum of all angles on one side of a straight line AB at a point
O by any number of lines joining the line AB at O is 180°.
(v) When any number of straight lines joining at a point, then the
sum of all the angles around that point is 360° which is called as
complete angle.
(vi) Two angles whose sum is 90° are said to be complementary to
each other and two angles whose sum is 180° are said to be
supplementary to each other.
Intersecting Lines
When two straight lines intersect each other, then vertically opposite
angles are equal.
l2
1
2 O 4
3
l1
i.e. ∠ 1 = ∠ 3, ∠ 2 = ∠ 4
Parallel Lines
When a straight line XY cuts two parallel lines l1 and l2 as shown in
the figure, the line XY is called the transversal line.
X
2 1
l2
3 4
6 5
l1
7 8
Y
The following are the relationships between various angles that are
formed.
(i) Alternate angles are equal.
i. e. ∠ 1 = ∠ 7,∠ 2 = ∠ 8, [alternate exterior angles]
∠ 3 = ∠ 5 and ∠ 4 = ∠ 6. [alternate interior angles]
(ii) Corresponding angles are equal.
i. e. ∠ 1 = ∠ 5, ∠ 2 = ∠ 6, ∠ 3 = ∠ 7 and ∠ 4 = ∠ 8.
(iii) Sum of interior angles on the same side of the transversal line is
equal to 180°.
i. e. ∠ 3 + ∠ 6 = 180° and ∠4 + ∠5 = 180°
This is also known as cointerior angles.
Point
A fine dot on paper or a location on plane is called point. Point has no
length, breadth or thickness.
Line
A line is defined as a line of points that extends infinitely in both
directions.
P Q
Line Segment
A line segment is a part of line that is bounded by two distinct end
points and contains every point on the line between its end points.
A B
Ray
If a line segment is extended to unlimited length on one of the end
points, then it is called a ray.
A B
Important Points to be Remembered
(i) A line contains infinite points.
(ii) Infinite lines can pass through a point.
(iii) Two distinct lines in a plane cannot have more than one point common.
Angle
If two rays are drawn in different directions from y
a common initial point, then they are said to form Ra
an angle. Angle
O
(i) An angle of 90° is a right angle and an Ray
angle less than 90° is an acute angle.
(ii) An angle between 90° and 180° is an obtuse angle.
(iii) An angle between 180° and 360° is a reflex angle.
, (iv) The sum of all angles on one side of a straight line AB at a point
O by any number of lines joining the line AB at O is 180°.
(v) When any number of straight lines joining at a point, then the
sum of all the angles around that point is 360° which is called as
complete angle.
(vi) Two angles whose sum is 90° are said to be complementary to
each other and two angles whose sum is 180° are said to be
supplementary to each other.
Intersecting Lines
When two straight lines intersect each other, then vertically opposite
angles are equal.
l2
1
2 O 4
3
l1
i.e. ∠ 1 = ∠ 3, ∠ 2 = ∠ 4
Parallel Lines
When a straight line XY cuts two parallel lines l1 and l2 as shown in
the figure, the line XY is called the transversal line.
X
2 1
l2
3 4
6 5
l1
7 8
Y
The following are the relationships between various angles that are
formed.
(i) Alternate angles are equal.
i. e. ∠ 1 = ∠ 7,∠ 2 = ∠ 8, [alternate exterior angles]
∠ 3 = ∠ 5 and ∠ 4 = ∠ 6. [alternate interior angles]
(ii) Corresponding angles are equal.
i. e. ∠ 1 = ∠ 5, ∠ 2 = ∠ 6, ∠ 3 = ∠ 7 and ∠ 4 = ∠ 8.
(iii) Sum of interior angles on the same side of the transversal line is
equal to 180°.
i. e. ∠ 3 + ∠ 6 = 180° and ∠4 + ∠5 = 180°
This is also known as cointerior angles.
