Related Topics:

Lesson Plans and Worksheets for Geometry

Lesson Plans and Worksheets for all Grades

More Lessons for Geometry

Common Core For Geometry

Worksheets for Geometry, Module 1, Lesson 31

Student Outcomes

- Students learn to construct a square and begin to construct a nine-point circle.

**Construct a Square and a Nine-Point Circle**

Classwork

**Opening Exercise**

With a partner, use your construction tools and what you learned in Lessons 1β5 to attempt the construction of a square. Once you are satisfied with your construction, write the instructions to perform the construction.

**Exploratory Challenge**

Now, we are going to construct a nine-point circle. What is meant by the phrase nine-point circle?

Steps to construct a nine-point circle:

- Draw a triangle π΄π΅πΆ.
- Construct the midpoints of the sides π΄π΅ , π΅πΆ, and πΆπ΄ , and label them as πΏ, π, and π, respectively.
- Construct the perpendicular from each vertex to the opposite side of the triangle (each is called an altitude).
- Label the intersection of the altitude from πΆ to π΄π΅ as π·, the intersection of the altitude from π΄ to π΅πΆΜ Μ Μ Μ as πΈ, and of the altitude from π΅ to πΆπ΄ as πΉ.
- The altitudes are concurrent at a point; label it π».
- Construct the midpoints of π΄π», π΅π», πΆπ», and label them π, π, and π, respectively.
- The nine points, πΏ, π, π, π·, πΈ, πΉ, π, π, π, are the points that define the nine-point circle.

**Example**

On a blank white sheet of paper, construct a nine-point circle using a different triangle than you used during the notes. Does the type of triangle you start with affect the construction of the nine-point circle?

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.