MathIsimple

Lines & Angles

Master the fundamentals of geometry: learn about lines, rays, segments, angle types, angle relationships, parallel lines, perpendicular lines, and transversals.

Geometry
Beginner
~45 min
Angle Calculator
Find complementary, supplementary, or missing triangle angles
1. Lines, Rays, and Segments

Line

Extends infinitely in both directions. Has no endpoints.

←————————→

Notation: AB↔\overleftrightarrow{AB}

Ray

Has one endpoint, extends infinitely in one direction.

A•————————→

Notation: AB→\overrightarrow{AB}

Line Segment

Has two endpoints. A finite portion of a line.

A•————————•B

Notation: AB‾\overline{AB} or AB

2. Types of Angles

Acute Angle

Measures between 0°0° and 90°90°

Right Angle

Measures exactly 90°90°

Obtuse Angle

Measures between 90°90° and 180°180°

Straight Angle

Measures exactly 180°180° (a straight line)

Reflex Angle

Measures between 180°180° and 360°360°

Full Rotation

Measures exactly 360°360° (complete circle)

3. Angle Relationships

Complementary Angles

∠A+∠B=90°\angle A + \angle B = 90°

Two angles that sum to 90°. Example: 30° and 60° are complementary.

Supplementary Angles

∠A+∠B=180°\angle A + \angle B = 180°

Two angles that sum to 180°. Example: 110° and 70° are supplementary.

Vertical Angles

∠1=∠3,∠2=∠4\angle 1 = \angle 3, \quad \angle 2 = \angle 4

When two lines intersect, opposite angles are equal.

Adjacent Angles

Angles that share a common vertex and a common side, but do not overlap. They are "next to" each other.

4. Parallel Lines & Transversals

Parallel Lines

Two lines in the same plane that never intersect, no matter how far they are extended. Notation: ℓ1∥ℓ2\ell_1 \parallel \ell_2

Corresponding Angles

Same position at each intersection. Equal when lines are parallel.

∠1 = ∠5, ∠2 = ∠6, etc.

Alternate Interior Angles

On opposite sides of transversal, inside the parallel lines. Equal.

∠3 = ∠6, ∠4 = ∠5

Alternate Exterior Angles

On opposite sides of transversal, outside the parallel lines. Equal.

∠1 = ∠8, ∠2 = ∠7

Co-interior Angles

Same side of transversal, inside the parallel lines. Supplementary (sum to 180°).

∠3 + ∠5 = 180°, ∠4 + ∠6 = 180°
5. Perpendicular Lines
ℓ1⊥ℓ2  ⟺  They intersect at 90°\ell_1 \perp \ell_2 \iff \text{They intersect at } 90°

Perpendicular lines intersect to form four right angles.

Properties

  • All four angles at intersection are 90°
  • Shortest distance from a point to a line is perpendicular
  • Used to construct altitudes in triangles

Real-World Examples

  • • Corners of rectangular rooms
  • • Graph paper grid lines
  • • Street intersections (typically)
  • • Wall meets floor at 90°

Practice Quiz

Practice Quiz
20
Questions
0
Correct
0%
Accuracy
1
What is a line in geometry?
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2
What is a ray?
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3
What is a line segment?
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4
Two angles that sum to 90°90° are called:
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5
Two angles that sum to 180°180° are called:
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6
When two lines intersect, the opposite angles are called:
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7
If two lines are parallel, what can we say about their intersection?
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8
Two lines that intersect at a 90°90° angle are called:
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9
If angle A and angle B are vertical angles and angle A = 65°65°, what is angle B?
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10
If two angles are supplementary and one angle is 110°110°, what is the other angle?
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11
When a transversal crosses two parallel lines, corresponding angles are:
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12
Alternate interior angles formed by a transversal crossing parallel lines are:
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13
An angle measuring exactly 90°90° is called:
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14
An angle measuring between 0°0° and 90°90° is called:
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15
An angle measuring between 90°90° and 180°180° is called:
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16
A straight angle measures:
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17
Co-interior angles (same-side interior angles) formed by a transversal crossing parallel lines are:
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18
If angle A = 35°35° and angle B is its complement, what is angle B?
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19
How many degrees are in a full rotation?
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20
If two parallel lines are cut by a transversal and one angle is 72°72°, how many of the eight angles formed are 72°72°?
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