# Intersecting Chords Theorem Activities

Instructor: Heather Jenkins

Heather has a bachelor's degree in elementary education and a master's degree in special education. She was a public school teacher and administrator for 11 years.

The intersecting chords theorem can be used to help students understand the relationship between the segments of intersecting chords. Use these multi-sensory activities to help students learn how to use the intersecting chords theorem.

## Distances Inside a Circle

The intersecting chords theorem helps define how far away a certain point inside a circle is from various other points on a circle. When students learn about the mathematical relationship between the segments of intersecting chords, it can help them calculate distances inside a circle. Let's look at some activities to help students understand the intersecting chords theorem.

## Human Chord Theorem

Have students use their bodies and yarn to prove the intersecting chords theorem.

### Materials

• Yarn
• Rulers/meter sticks
• Paper
• Pencils

### Teacher Directions

1. Draw a circle with two chords and discuss the intersecting chords theorem. Discuss how the products of the segments of two intersecting chords are equal.
2. Tell the class that they are going to recreate the theorem using their bodies and yarn.
3. Go to a location in your school where there is already a circle on the ground, such as the gym.
4. Have students stand around the circle.
5. Give a piece of yarn to two students in the circle to form a chord. Create another chord, in the same manner, which intersects the first chord.
6. Select other students to use rulers/meter sticks to measure the segments of each piece of yarn from the point of intersection to the student's hands. Students will then plug these values into the intersecting chord theorem to prove that the products of the segments of the intersecting chords are equal.
7. Have students repeat this with different students creating the chords and taking the measurements.

### Discussion Questions

• What is the relationship between the segments formed by two intersecting chords?
• What might account for small variations between the values we calculated and the expected values from the intersecting chords theorem?

## Dreamcatcher Theorem

Engage students' creative sides as they create dream catchers to practice using the intersecting chords theorem.

### Materials

• Dreamcatcher
• Small embroidery hoops
• Yarn
• Rulers
• Feathers
• Scissors
• Glue
• Paper
• Pencils

### Teacher Directions

1. Show the class a dreamcatcher. Ask the students to identify various chords created by the yarn in the dreamcatcher.
2. Review the intersecting chords theorem with the class.
3. Provide each student with an embroidery hoop, yarn, feathers, beads, scissors, and glue.
4. Demonstrate how to make a dream catcher by wrapping yarn around the embroidery hoop and through the circle at various locations to create a web-like structure inside the hoop. Students can add feathers to their dreamcatchers.
5. Have students select five different colored beads. Students should glue these beads at five different locations on the dream catcher where strings/chords intersect.
6. Provide each student with paper and pencils.
7. Have students prove the intersecting chord theorem for the segments of the intersecting chords located at each colored bead. Students will measure the segments created by the chords and compare their products to the expected values of the intersecting chord theorem.
8. When finished, students should share their dreamcatchers and findings with the class.

### Discussion Questions

• Does the intersecting chord theorem apply no matter where the chords are located on the circle? Why or why not?
• How might this theorem be useful in real-life situations?

## Where's the Boat?

Have students use the intersecting chords theorem to figure out the distance the boat must travel to its destination.

### Materials

• Picture of a circular lake
• Blue construction paper
• Chart paper
• Compass
• Pencils
• Scissors
• Glue
• Tape
• Markers
• Rulers
• Paper

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