Lines and Angles parallel lines, a transversal, and all types of angles

1. What are Lines?

• A line is a straight path that extends infinitely in both directions.

• Line segment: Part of a line between two points.

• Ray: Part of a line that starts at one point and goes infinitely in one direction.

2. Types of Lines

1. Intersecting Lines: Lines that cross each other at one point.

2. Parallel Lines: Lines that never meet, no matter how far they are extended.

3. Perpendicular Lines: Lines that intersect at a right angle (90°).

3. What are Angles?

• An angle is formed when two rays meet at a common point (called the vertex).

• Angles measure the turn between the two rays.

4. Types of Angles

1. Acute Angle: Less than 90°

2. Right Angle: Exactly 90°

3. Obtuse Angle: Greater than 90° but less than 180°

4. Straight Angle: Exactly 180°

5. Reflex Angle: Greater than 180° but less than 360°

5. Angles Made by a Transversal

• A transversal is a line that crosses two or more lines.

• Important angles formed:

  1. Corresponding Angles → same relative position on the two lines

  2. Alternate Interior Angles → inside the lines, on opposite sides of transversal

  3. Alternate Exterior Angles → outside the lines, on opposite sides of transversal

  4. Co-Interior (Consecutive Interior) Angles → inside the lines, on the same side of transversal

Note:

• If the two lines are parallel, the corresponding angles and alternate interior angles are equal.

• Co-interior angles are supplementary (sum up to 180°).

6. Important Points for Exams

• Lines: intersecting, parallel, perpendicular

• Angles: acute, right, obtuse, straight, reflex

• Transversal → line cutting two lines → forms special angle pairs

• Angle relationships help in geometry proofs and problem solving