# Eureka Math Geometry Module 1 Lesson 32 Answer Key

## Engage NY Eureka Math Geometry Module 1 Lesson 32 Answer Key

### Eureka Math Geometry Module 1 Lesson 32 Opening Exercise Answer Key

Opening Exercise:

During this unit, we have learned many constructions. Now that you have mastered these constructions, write a list of advice for someone who is about to learn the constructions you have learned for the first time. What did and did not help you? What tips did you wish you had at the beginning that would have made It easier along the way?

### Eureka Math Geometry Module 1 Lesson 32 Exploratory Challenge Answer Key

Exploratory Challenge 1:

Yesterday, we began the nine-point circle construction. What did we learn about the triangle that we start our construction with? Where did we stop in the construction? We continue our construction today.
There are two constructions for finding the center of the nine-point circle. With a partner, work through both constructions.

Construction 1:
1. To find the center of the circle, draw inscribed ∆LMN.
2. Find the circumcenter of ∆LMN, and label it as U.
Recall that the circumcenter of a triangle is the center of the circle that circumscribes the triangle, which, in this case, is the nine-point circle.

Construction 2:
1. Construct the circle that circumscribes ∆ABC.
2. Find the circumcenter of ∆ABC, which is the center of the circle that circumscribes ∆ABC. Label its center CC.
3. Draw the segment that joins point H (the orthocenter from the construction of the nine-point circle in Lesson 31) to the point CC.
4. Find the midpoint of the segment you drew in Step 3, and label that point U.

Describe the relationship between the midpoint you found in Step 4 of the second construction and point U in the first construction.
The center U is the midpoint of the segment from the orthocenter H to CC.

Exploratory Challenge 2:

Construct a square ABCD. Pick a point E between B and C, and draw a segment from point A to point E. The segment forms a right triangle and a trapezoid out of the square. Construct a nine-point circle using the right triangle.

### Eureka Math Geometry Module 1 Lesson 32 Problem Set Answer Key

Question 1.
Take a blank sheet of 8$$\frac{1}{2}$$ inch by the 11-inch white paper, and draw a triangle with vertices on the edge of the paper. Construct a nine-point circle within this triangle. Then, draw a triangle with vertices on that nine-point circle, and construct a nine-point circle within that. Continue constructing nine-point circles until you no longer have room inside your constructions.