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.
Angles that are across from each other are equal (× pattern).
Any two angles whose measures sum to 180°. In the original diagram, ∠A + ∠B = 180° (though other examples also exist).
Angle pairs whose measures sum to one right angle (90°). This is not illustrated in the example above.
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).
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).
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.
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