Mathematics Notes for Class 11 Lines And-Angles

Lines and Angles

Welcome to the chapter on Lines and Angles for Class 11. In this chapter, you will learn about different types of lines and angles, their properties, and how to solve problems using these concepts. By the end of this chapter, you will be able to identify, measure, and use lines and angles in geometry.

Key Concepts

Line: A straight path that extends endlessly in both directions.
Line Segment: A part of a line with two endpoints.
Ray: A part of a line that starts at one point and extends endlessly in one direction.
Angle: Formed when two rays meet at a common endpoint (vertex).

Types of Angles

Acute Angle: Less than 90°
Right Angle: Exactly 90°
Obtuse Angle: Greater than 90° but less than 180°
Straight Angle: Exactly 180°
Reflex Angle: Greater than 180° but less than 360°
Complete Angle: Exactly 360°

Pairs of Angles

Complementary Angles: Two angles whose sum is 90°.
Supplementary Angles: Two angles whose sum is 180°.
Adjacent Angles: Two angles that have a common vertex and a common arm but do not overlap.
Linear Pair: A pair of adjacent angles whose non-common arms form a straight line.
Vertically Opposite Angles: Angles opposite each other when two lines cross. They are always equal.

Properties of Lines and Angles

The sum of angles on a straight line is 180°.
The sum of angles around a point is 360°.
Vertically opposite angles are equal.
If two lines intersect, the opposite angles are equal.
If two lines are parallel, alternate interior angles are equal, and corresponding angles are equal.

Parallel Lines and Transversal

When a line (called a transversal) crosses two parallel lines, several pairs of angles are formed:

Corresponding Angles: Equal in measure.
Alternate Interior Angles: Equal in measure.
Alternate Exterior Angles: Equal in measure.
Consecutive Interior Angles: Their sum is 180°.

Practice Questions

Define complementary and supplementary angles with examples.
If two angles form a linear pair and one angle is 70°, what is the other angle?
If two parallel lines are cut by a transversal and one corresponding angle is 110°, find all other angles formed.
Prove that vertically opposite angles are equal when two lines intersect.
If the sum of two adjacent angles is 180°, what type of angles are they?

Challenge Yourself

Draw two parallel lines and a transversal. Mark all pairs of corresponding, alternate interior, and alternate exterior angles.
If the supplement of an angle is three times its complement, find the angle.

Did You Know?

The word "angle" comes from the Latin word "angulus," meaning "corner."
Angles are used in architecture, engineering, and even art!

Glossary

Transversal: A line that crosses at least two other lines.
Parallel Lines: Lines that never meet and are always the same distance apart.
Vertex: The common endpoint of two rays forming an angle.
Linear Pair: A pair of adjacent angles whose non-common sides form a straight line.

Answers to Practice Questions

Complementary angles: Two angles whose sum is 90° (e.g., 30° and 60°). Supplementary angles: Two angles whose sum is 180° (e.g., 110° and 70°).
The other angle is 110° (since 180° - 70° = 110°).
All corresponding angles are 110°, alternate interior angles are 110° and 70°, and the other angles are 70°.
When two lines intersect, the opposite angles are equal because they are formed by the same pair of lines.
They are supplementary angles (linear pair).

Understanding lines and angles is the foundation of geometry. Practice drawing and measuring angles to master this topic!

Mathematics Class 11 - Lines And-Angles Notes