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Door 15 ยท Grade 4

๐Ÿ“ Lines and Angles

Parallel lines: never meet, always same distance apart (like train tracks)

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Types of Lines

In geometry, a line is a straight path. In Grade 4, we study three important relationships between lines:
โ€ข Parallel Lines: Lines that never meet and are always the same distance apart. Like railway tracks or opposite edges of a ruler.
โ€ข Perpendicular Lines: Lines that meet at exactly 90 degrees (a right angle). Like the corner of a room or the letter L.
โ€ข Intersecting Lines: Lines that cross each other at any angle. Like scissors or roads crossing at a junction.

A line segment has two endpoints. A ray has one endpoint and goes on forever in one direction.

Worked example

Problem: Identify the type of lines formed by the two vertical bars in the letter 'H'.

  1. The two vertical lines in 'H' are parallel โ€” they run in the same direction, are always the same distance apart, and never meet.

Answer: The two vertical lines in 'H' are parallel โ€” they run in the same direction, are always the same distance apart, and never meet.

Types of Angles

An angle is formed when two rays meet at a common point called the vertex. Angles are measured in degrees (ยฐ).
Three main types of angles:
โ€ข Acute Angle: Less than 90 degrees (sharp, like the tip of a pencil)
โ€ข Right Angle: Exactly 90 degrees (like the corner of a square)
โ€ข Obtuse Angle: Between 90 and 180 degrees (wider than a right angle)

A straight angle = 180 degrees (a straight line).

Worked example

Problem: Classify these angles: 45 degrees, 90 degrees, 135 degrees.

  1. 45 degrees: Acute (less than 90).
  2. 90 degrees: Right angle (exactly 90).
  3. 135 degrees: Obtuse (between 90 and 180).

Answer: 135 degrees: Obtuse (between 90 and 180).

Using a Protractor to Measure Angles

A protractor is the tool used to measure angles in degrees.
Steps to measure an angle with a protractor:
โ€ข Place the centre hole of the protractor at the vertex of the angle
โ€ข Align the baseline (0 line) with one ray of the angle
โ€ข Read the degrees where the second ray crosses the scale
โ€ข Use the scale that starts from 0 on the side where you placed the baseline

Protractors have two scales โ€” always use the correct one!

Worked example

Problem: Describe the steps to draw a 60 degree angle.

  1. Step 1: Draw a ray.
  2. Step 2: Place protractor centre at the endpoint (vertex).
  3. Step 3: Align baseline with the ray.
  4. Step 4: Mark a point at 60 degrees on the scale.
  5. Step 5: Connect the vertex to that point with another ray.

Answer: Step 5: Connect the vertex to that point with another ray.