1. Check it out! 1.2.1: Copying Segments and Angles
1.2.1: Copying Segments and Angles

2. Maryellen is caring for a pet goat
Maryellen is caring for a pet goat. To keep the goat from roaming the neighborhood, Maryellen ties the goat to a leash staked in the yard. Maryellen learned quickly that goats enjoy chewing grass, so she must change the location of the stake periodically.
The original location of the stake is shown on the next slide, on the left with the leash stretched out. Maryellen moved the stake to a new location, shown on the right. Use the diagrams to solve the problems that follow.
Common Core Georgia Performance Standard: MCC9–12.G.CO.12
1.2.1: Copying Segments and Angles

3. Original stake location
New stake location
Using only a compass, determine if there will be an overlap in the area the goat will chew.
Maryellen wants to keep both her goat and her yard healthy. Describe a process for determining where Maryellen should place each new stake in order to prevent the goat from overgrazing on the same patch of grass.
Common Core State Standard: G–CO.12
1.2.1: Copying Segments and Angles

4. Open the compass so the pencil point reaches the end of the leash.
Using only a compass, determine if there will be an overlap in the area the goat will chew.
First, put the sharp point of the compass at the original stake location.
Open the compass so the pencil point reaches the end of the leash.
Draw a circle, keeping the sharp point at the original stake location.
1.2.1: Copying Segments and Angles

5. Original stake location
New stake location
1.2.1: Copying Segments and Angles

6. Draw a circle, keeping the sharp point at the new stake location.
Without adjusting the opening of the compass, place the sharp point of the compass on the new stake location.
Draw a circle, keeping the sharp point at the new stake location.
1.2.1: Copying Segments and Angles

7. Original stake location
New stake location
The circles do not overlap; therefore, the areas chewed by the goat will not overlap.
1.2.1: Copying Segments and Angles

8. Maryellen wants to keep both her goat and her yard healthy
Maryellen wants to keep both her goat and her yard healthy. Describe a process for determining where Maryellen should place each new stake in order to prevent the goat from overgrazing on the same patch of grass.
Using the leash that has already been staked, Maryellen could mark the area the goat can chew by pulling the leash tight and walking the circle.
Maryellen could then place one end of the leash on the outside edge of the circle, untie the leash from the stake, and stretch the leash out in the opposite direction from where the goat was staked.
1.2.1: Copying Segments and Angles

9. She could then place the stake in the ground.
The leash acts like a compass for determining the circle.
Maryellen could continue doing this to minimize the amount of overlap, and ensure that she uses the space in her yard the most effectively.
Connection to the Lesson
• Students will practice using a compass to make circles.
• It is important that students are capable of creating circles effortlessly before proceeding.
• Students will determine lengths with tools other than rulers.
1.2.1: Copying Segments and Angles