Lines and Angles

What is a Line?

Line: A straight path that goes on forever in both directions

• Has NO endpoints
• Named with two points and a line symbol: ↔
• Example: Line AB (written as AB with line symbol)

Line segment: Part of a line with TWO endpoints

• Has a definite length you can measure
• Example: Segment AB (written as AB with a bar)

Ray: Part of a line with ONE endpoint and goes on forever in one direction

• Like a sun ray!
• Example: Ray AB (written as AB with arrow on top)

Types of Lines

Parallel lines: Lines that never cross (intersect)

• Always the same distance apart
• Like railroad tracks: ═══
• Symbol: ∥

Perpendicular lines: Lines that cross at right angles (90°)

• They make a square corner where they meet
• Like a plus sign: +
• Symbol: ⊥

Intersecting lines: Lines that cross each other

• They meet at one point
• Example: X

What is an Angle?

Angle: Formed when two rays share the same endpoint

Parts of an angle:

• Vertex: The point where two rays meet
• Rays: The two sides of the angle
• Measure: How far apart the rays are (measured in degrees °)

Types of Angles

Right angle: Exactly 90°

• Makes a square corner
• Like the corner of a book: L
• Symbol: Small square in the corner

Acute angle: Less than 90°

• A "cute" little angle (small)
• Sharp and pointy: /

Obtuse angle: More than 90° but less than 180°

• A big, wide angle: \

Straight angle: Exactly 180°

• Makes a straight line: ―

Measuring Angles

We measure angles with a protractor

Steps to use a protractor:

1. Place the center hole on the vertex
2. Line up one ray with the 0° line
3. Read where the other ray points
4. That number is your angle measure!

Remember:

• Most protractors have two sets of numbers
• Use the set that starts at 0° where your first ray is
• Read from inside to outside

Drawing Angles

To draw an angle:

1. Draw one ray (use a ruler)
2. Place protractor at the endpoint
3. Find your degree measurement
4. Mark a point there
5. Connect the endpoint to the mark
6. Label your angle!

Angle Pairs

Adjacent angles: Angles next to each other that share a ray

• Like two puzzle pieces side-by-side

Vertical angles: Opposite angles formed when two lines cross

• They're always equal!
• Like an X - the opposite angles are the same

Real-World Examples

Right angles (90°):

• Corners of a room
• Corner of a piece of paper
• Where the floor meets the wall

Acute angles:

• Hands on a clock at 1:00
• Roof of a house
• Piece of pizza slice

Obtuse angles:

• Hands on a clock at 10:00
• Open laptop
• Reclined chair

Straight angles:

• Horizon line
• Flat road
• Ruler edge

Practice Tips

To identify angle types:

• Compare to a square corner (right angle = 90°)
• If smaller than square corner → acute
• If exactly a square corner → right
• If bigger than square corner → obtuse
• If makes a straight line → straight

Estimating angles:

• Right angle = 90° (easy to remember!)
• Half a right angle ≈ 45°
• One and a half right angles ≈ 135°
• Two right angles = 180° (straight line)

Common Mistakes

❌ Measuring from the wrong 0° on the protractor ❌ Reading the wrong set of numbers ❌ Calling any corner a "right angle" (it must be exactly 90°!) ❌ Thinking all angles in a shape are the same

✅ Always start from 0° when measuring ✅ Check which set of numbers to use ✅ Use the square symbol to mark right angles ✅ Measure carefully!