Lines & Angles Summary Class 7 NCERT Summary Chapter 1

Recall

• A Point means a location.
• A line is a straight that extends endlessly in both directions.

• A line segment is the part of a line between two points.

• A ray is part of a line that starts at one point and extends endlessly in another direction.

• An angle is formed when lines or line segments meet.

Related Angles

• When the sum of the measures of two angles is 90°, the angles are called complementary angles.
• Whenever two angles are complementary, each angle is said to be the complement of the other angle.

Complementary Angles

• When the sum of the measures of two angles is 180°, the angles are called Supplementary angles.
• When two angles are supplementary, each angle is said to be the supplement of the other.

Supplementary Angles

• Two angles with a common vertex and common arm but no common interior points are called Adjacent angles.
• These angles are such that:
  (i) they have a common vertex;
  (ii) they have a common arm; and
  (iii) the non-common arms are on either side of the common arm.
• A linear pair is a pair of adjacent angles whose non-common sides are opposite rays.
• Vertically Opposite Angles: Two angles formed by two intersecting lines having no common arm. When two lines intersect, the vertically opposite angles so formed are equal.

Pair of Lines

• Intersecting Lines: Two or more lines that have one and only one point in common. The common point where all the intersecting lines meet is called the point of intersection.
• A line that intersects two or more lines at distinct points is called a transversal.
• Parallel lines: Two lines in the same plane that are at equal distance from each other and never meet.
• Alternate interior angle : The pair of angles on opposite sides of the transversal but inside the two lines are called alternate interior angles.
• Alternate exterior angle : The pair of angles on the opposite sides of the transversal but outside the two lines are called alternate exterior angles
• When two lines are intersected by a transversal, eight angles are formed.

Interior angles: ∠3, ∠4, ∠5, ∠6
Exterior angles: ∠1, ∠2, ∠7, ∠8
Pairs of corresponding angles: ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8
Pairs of Alternate interior angles: ∠3 and ∠6, ∠4 and ∠5
Pairs of Alternate exterior angles: ∠1 and ∠8, ∠2 and ∠7
Pairs of interior angles on the same side of the transversal: ∠3 and ∠5, ∠4 and ∠6.

Transversal of parallel lines

If two parallel lines are intersected by a transversal, each pair of:

• corresponding angles are congruent
• alternate interior angles are congruent
• alternate exterior angles are congruent
• interior angles on the same side of the transversal are supplementary.