Identify, measure, and calculate different types of straight lines and angles

Much of this section can be summarized using the diagram:

Notice how lines 1 and 2 (denoted L1 and L2) are parallel (they never intersect), and that’s indicated by red arrows. Line T is called the transversal, it simply cuts through L1 and L2. How each of these angles are related is explained below.

Opposite Angles

Angles that are across from each other are equal (× pattern).

  • Using the diagram above:
    • ∠A = ∠D
    • ∠C = ∠B
    • ∠E = ∠H
    • ∠G = ∠F
  • Generally:


Supplementary Angles

Any two angles whose measures sum to 180°. In the original diagram, ∠A + ∠B = 180° (though other examples also exist).

  • Generally:

Complementary Angles

Angle pairs whose measures sum to one right angle (90°). This is not illustrated in the example above.

  • Generally:

Corresponding Angles

When two parallel lines are crossed by the transversal, the angles in matching corners are equal (F pattern). In the original diagram, ∠A are ∠E are equal (though other examples also exist).

  • Generally:

Alternate Interior Angles

Two interior angles which lie on different parallel lines and on opposite sides of a transversal are equal (Z pattern). In the original diagram, ∠E are ∠D are equal (though other examples also exist).

  • Generally:

Co-interior Angles

Angles on the same side of the transversal and inside the parallel lines are supplementary (both angles add up to 180°).

  • Using the same diagram we started with, ∠C and ∠E summed up should equal to 180°. Algebraically, this can be represented as ∠C + ∠E = 180°.

A summary on parallel lines is shown below:

Examples where we apply these rules are shown below:

  • Part 2, Part 3, and Part 4 can be accessed by clicking each link. Parts 3 and 4 incorporate algebraic expressions into the mix. It’s just another example displaying the versatility of algebra found across many fields of mathematics.

Corresponding Segments

When a number of parallel lines are cut by two transversals, the portions of the transversals lying between the same parallels are called corresponding segments.

Let’s apply this to a real-life situation:

Question: A portion of a street map is shown. Find the distances PQ and QR.

Solution: The transversal lines are Avenue A and B. Start by comparing these two sides via a fraction: null

This fraction is then made equal to 172 over PQ: null

To solve, you can cross-multiply to get 195 feet. Similarly, to find QR: null