Learn

Town Project

This lesson is a project that you will create using parallel lines and transversals. This project will be unique from what you have learned so far because we will be adding an extra parallel line and transversal.

Criteria Sample

Certain criteria will be given for you to follow when you construct your town such as the sample below:

  • The school and your house are alternate exterior angles.
  • The grocery store and gas station is a linear pair of angles.
  • The town hall and church are vertical angles.
  • The post office and town hall are corresponding angles.
  • The grocery store and restaurant are alternate interior angles.
  • The shopping center and barber shop are same side exterior angles.

Instructions

Up to this point you have only worked with one pair of parallel lines and one transversal so this presentation will help guide you with some examples of what to do and what not to do. When placing your buildings on your diagram you must narrow down your diagram by choosing two parallel lines and one transversal. Your interactive will allow you to hide the lines you are not working with so that you can better see the angle relationship.

Example #1 - Incorrect

Let’s take a look at the first bullet from the sample criteria we listed earlier. The school and your house are alternate exterior angles. Below is an example of incorrect way to do this.

Why is it incorrect? These buildings are on angles formed by two different transversals. You can use any combination of the parallel lines. But you must use the same transversal.

lines d and e intersecting horizontal lines a ,b, and c; the word house in between the rays of the top-left angle that is formed by lines d and a; the word school is between the rays of the bottom-right angle that is formed by lines e and c

Example #1 - Correct

The school and your house are alternate exterior angles. Below is the correct way using the same transversal. Notice that I used the lines a and c as my parallel lines. I could have chosen lines a and b, then the park would have moved up one line. In other words, there can be multiple ways to create your town.

lines d and e intersecting horizontal lines a ,b, and c; the word house in between the rays of the top-left angle that is formed by lines d and a; the word school is between the rays of the top-left angle that is formed by lines e and c; the word park is between the rays of the bottom-right angle that is formed by lines d and c

Important

Again, it is important that you choose two parallel lines and one transversal. Hide the other lines so that it is easier to find the angle relationship. A virtual worksheet will be provided that allows you to practice before creating for final town. You will notice that certain buildings appear more than once in your criteria, such as the school. When you put the school on your grid for the first criteria, that position may not work the next time it comes up. It is important that you try several variations because you may need to try several times to solve this puzzle.

Building Location

Make sure buildings are located in the angles and not in the middle of the road. There is no way to tell which angle the house is in with this location.

lines d and e intersecting horizontal lines a ,b, and c; the word house in between lines d and e and on top of line a

Rough Draft

The following are roungh drafts of our earlier example.

The school and your house are alternate exterior angles.

lines d and e intersecting horizontal lines a ,b, and c; the word school is between the rays of the top-right angle formed by lines d and a; the word house is between the rays of the bottom-left angle formed by lines d and c

The gas station and grocery are a linear pair of angles.

lines d and e intersecting horizontal lines a ,b, and c; the words gas station is between the rays of the bottom-left angle formed by lines d and b; the word grocery is between the rays of the bottom-right angle formed by lines d and b

The town hall and church are vertical angles.

lines d and e intersecting horizontal lines a ,b, and c; the words town hall is between the rays of the top-right angle formed by lines e and c; the word church is between the rays of the bottom-left angle formed by lines e and c

The post office and town hall are corresponding angles.

lines d and e intersecting horizontal lines a ,b, and c; the words post office is between the rays of the top-right angle formed by lines e and b’ the words town hall is between the rays of the top-right angle formed by lines e and c

The grocery and restaurant are alternate interior angles.

lines d and e intersecting horizontal lines a ,b, and c; the word grocery is between the rays of the bottom-right angle formed by lines d and b; the word restaurant is between the rays of the top-left angle formed by lines d and c

The shopping center and barber shop are same side exterior angles.

lines d and e intersecting horizontal lines a ,b, and c; the words shopping center is between the rays of the top-right angle formed by lines e and a; the words barber shop is between the rays of the bottom-right angle formed by lines e and c