Lines and Angles • Topic 1 of 3

Intersecting and Non-Intersecting Lines; Angle Pairs

What are Intersecting and Non-Intersecting Lines?

  • Intersecting lines are lines that cross each other at exactly one point (called the point of intersection)
  • Non-intersecting lines (parallel lines) are lines that never meet, no matter how far they are extended

What are Different Angle Pairs?

When two lines intersect or when lines are combined, various angle pairs are formed:

Angle PairDefinitionDiagram DescriptionProperty
**Supplementary Angles**Two angles whose sum is 180°110° + 70° = 180°Each is supplement of the other
**Adjacent Angles**Two angles sharing a common vertex and common arm, with non-common arms on opposite sidesAngles next to each otherThey do not overlap
**Linear Pair**Adjacent angles formed when two lines intersect; their non-common arms are opposite rays∠AOC and ∠COB sharing ray OCSum = 180°
**Vertically Opposite Angles**Angles opposite each other when two lines intersect∠AOC and ∠BODThey are always EQUAL

Real-Life Examples:

  • Intersecting lines: Crossroads, scissors, window grills
  • Parallel lines: Railway tracks, opposite edges of a notebook
  • Complementary angles: Acute angles in a right triangle, clock hands at 3:00 (90°)
  • Linear pair: Door opening, book pages
Types of Angle PairsComplementary∠A+∠B=90°Supplementary∠A+∠B=180°Vertically Opp.∠1=∠3, ∠2=∠4Linear PairAdjacent + supp.35°55°120°60°∠1∠1∠2∠2180°Adjacent angles share a vertex and a common arm (no overlap)Vertically opposite angles are ALWAYS equal — key theorem
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Worked Example

Solve a standard problem on Intersecting and Non-Intersecting Lines; Angle Pairs.

Solution

Apply the formula/method shown in the concept section above.

Key Points

  • Understand the definition and properties of Intersecting and Non-Intersecting Lines; Angle Pairs.
  • Study the worked examples and practice similar problems.
  • Always verify your answer using the original conditions.
Tap an option to check your answer0 / 4
Q1.Two angles whose sum is $90^\circ$ are:
Explanation: Complementary.
Q2.Two angles whose sum is $180^\circ$ are:
Explanation: Supplementary.
Q3.Vertically opposite angles are:
Explanation: Always equal.
Q4.The angles of a linear pair add up to:
Explanation: A straight angle.