# Eureka Math Geometry Module 1 Lesson 2 Answer Key

## Engage NY Eureka Math Geometry Module 1 Lesson 2 Answer Key

### Eureka Math Geometry Module 1 Lesson 2 Exercise Answer Key

Opening Exercise
You need a compass, a straightedge, and another student’s Problem Set.
Directions:
Follow the directions from another student’s Problem Set write-up to construct an equilateral triangle.
→ What kinds of problems did you have as you followed your classmate’s directions?
→ Think about ways to avoid these problems. What criteria or expectations for writing steps in constructions should be included in a rubric for evaluating your writing? List at least three criteria.

### Eureka Math Geometry Module 1 Lesson 2 Exploratory Challenge Answer Key

Exploratory Challenge 1.
You need a compass and a straightedge.
Using the skills you have practiced, construct three equilateral triangles, where the first and second triangles share a common side and the second and third triangles share a common side. Clearly and precisely list the steps needed to accomplish this construction.
Switch your list of steps with a partner, and complete the construction according to your partner’s steps. Revise your drawing and list of steps as needed.
Construct three equilateral triangles here:

1. Draw a segment AB.
2. Draw circle A: center A, radius AB.
3. Draw circle B: center B, radius BA.
4. Label one intersection as C; label the other intersection as D.
5. Draw circle C: center C, radius CA.
6. Label the intersection of circle C with circle A (or the intersection of circle C with circle B) as E.
7. Draw all segments that are congruent to $$\overline{A B}$$ between the labeled points.

There are many ways to address Step 7; students should be careful to avoid making a blanket statement that would allow segment BE or segment CD.

Exploratory Challenge 2.
On a separate piece of paper, use the skills you have developed in this lesson to construct a regular hexagon. Clearly and precisely list the steps needed to accomplish this construction. Compare your results with a partner, and revise your drawing and list of steps as needed.

1. Draw circle K: center K, any radius.
2. Pick a point on the circle; label this point A.
3. Draw circle A: center A, radius AK.
4. Label the intersections of circle A with circle K as B and F.
5. Draw circle B: center B, radius BK.
6. Label the intersection of circle B with circle K as C.
7. Continue to treat the intersection of each new circle with circle K as the center of a new circle until the next circle to be drawn is circle A.
8. Draw $$\overline{A B}$$, $$\overline{B C}$$, $$\overline{C D}$$, $$\overline{D E}$$, $$\overline{E F}$$, $$\overline{F A}$$.

Can you repeat the construction of a hexagon until the entire sheet is covered in hexagons (except the edges, which are partial hexagons)?
Yes, this result resembles wallpaper, tile patterns, etc.

### Eureka Math Geometry Module 1 Lesson 2 Problem Set Answer Key

Why are circles so important to these constructions? Write out a concise explanation of the importance of circles in creating equilateral triangles. Why did Euclid use circles to create his equilateral triangles in Proposition 1? How does construction of a circle ensure that all relevant segments are of equal length?