Transversal Line and Angles

LESSON – TRANSVERSAL LINE AND ANGLES 

 

TOPIC
  • Introduction
  • Parallel Line
  • Transversal Line
  • Transversal Angles

 

INTRODUCTION 

A line is a straight or curved mark made by marking materials like pen, pencil, etc.

An angle is the space between two intersecting lines.

 

PARALLEL LINES 

Parallel lines are lines in a plane that are always the same distance apart like equal sign.

______________________

______________________

 

TRANSVERSAL LINES 

Transversal line are lines that intersect two straight lines or parallel lines at distinct points.

 

 

TRANSVERSAL ANGLES 

Transversal angles are angles formed when a straight line cuts the two parallel lines.

 

 

TRANSVERSAL ANGLES 

The following are transversal angles,

1. Corresponding angles

2. Alternate Interior Angles

3. Alternate Exterior Angles

4. Opposite Angles

 

CORRESPONDING ANGLES 

Corresponding angles are angles formed in the same position when a line cross the parallel lines.

 

 

In the above, all the following are corresponding angles –

 

  • A and E
  • C and G
  • B and F
  • D and H

 

ALTERNATE ANGLES 

Alternate angles are angles that are on the opposite sides of the transversal line.

All alternate angles are equal angles.

There are two (2) types of alternate angles, interior and exterior angles.

The angles formed inside the opposite sides are known are as interior angles. While angles formed outside opposite sides are known as exterior angles.

 

In the above, the following are alternate interior angles –

  • C and F
  • D and E

 

While, the following are alternate exterior angles –

  • A and H
  • B and G

 

OPPOSITE ANGLES 

Opposite angles are angles that are directly opposite to each on the transversal line.

These angles are equal angles and also known as vertical angles.

 

 

The following are vertical or opposite angles,

  • A and D
  • B and C
  • E and H
  • F and G

 

 CO – INTERIOR ANGLES 

Co – interior angles are angles between two parallel angles.

 

These are on the same sides of the transversal line.

The sum of the co – interior angles is equal to 180°.

 

 

In the above diagram, the following are co – interior angles –

  • D and F, D + F = 180°
  • C and E, C + E = 180°

 

SUPPLEMENTARY ANGLES 

Supplementary angles are two angles that are sum up to 180º on the transversal line.

 

 

Supplementary angles are as follows:

 

  • A and B, A + B = 180º
  • A and C
  • C and D
  • B and D, etc.

 

WORKING EXAMPLE

 

 

If A =46°, find the B, C, D, E, F, G and H.

 

 SOLUTIONS

If A = 46°, A + B = 180 (supplementary angles).

B = 180° – 46° = 134°

 

  • B = C = 134°(opposite angles)
  • A = D = 46° (opposite angles)
  • A = E = 46° (corresponding angles)
  • E = H = 46° (opposite angles)
  • B = F = 134° (corresponding angles)
  • F = G = 134° (corresponding angles)

Therefore, A = 46°, B = 134°, C = 134°, D =46°, E = 46°, F = 134°, G = 134° and H = 46°.

 

WORKING EXERCISE 

Find the letter a – g,

 

 

LESSON EVALUATION 

Answer 5 questions including number 6.

1. explain the meaning of angle.

2. list and explain types of angles.

3. different between transversal line and transversal angles.

4. draw a transversal line on parallel lines.

5. differentiate between transversal line and parallel lines.

 

6. Find the following letters,

 

 

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