Much of this section can be summarized using the diagram:

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

**Opposite Angles**

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

**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: nullThis 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