Chords and CirclesWith Patty Paper

(MCC9‐12.G.C.2; MCC9‐12.G.C.3; MCC9‐12.G.CO.9; MCC9‐12.G.CO.12)

Vertical angles are ≅;Chords and arcs are ≅.

© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Activities from Patty Paper® Geometry by Michael Serra

Steps:1.Draw a circle with

the Solo cup.2.Use your

straightedge to draw 2 chords as shown.

3.Label ∠1 and ∠2 as shown.

What do we know about the relationship between ∠1 and ∠2?

How can we prove that with our diagram?

1

2

© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Activities from Patty Paper® Geometry by Michael Serra

Steps:5.Fold the circle

where the sides of ∠1 meet the side of ∠2 .

What do you notice?

1

2

1

2

© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Activities from Patty Paper® Geometry by Michael Serra

Steps:6. Draw a chord for

each arc. 7. Compare the

chord lengths.

What do you notice? 1

2

© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Activities from Patty Paper® Geometry by Michael Serra

Diameter is the ⊥ bisectorof the chord.

© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Activities from Patty Paper® Geometry by Michael Serra

© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Activities from Patty Paper® Geometry by Michael Serra

Steps:1. Draw a circle with the

Solo cup.2. Use your straightedge

to draw 2 chords on your circle.

3. Fold to find the perpendicular bisector.

4. Place the corner of another piece paper at the angle formed between the chord and the perpendicular bisector.

What do you notice?

Central angles are ≅;Chords and arcs are ≅.

© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Activities from Patty Paper® Geometry by Michael Serra

© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Activities from Patty Paper® Geometry by Michael Serra

Steps:1. Draw a circle with

the Solo cup.2. Fold to find a

central angle.3. Place another

patty paper on top and copy the angle.

Steps:4. Copy this angle in

the original circle so that you have 2 central angles that are not vertical.

5. Compare the lengths of the arcs by folding.

Are they congruent?

6. Draw a chord for each arc.

7. Compare the chord lengths by folding.

© 2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Activities from Patty Paper® Geometry by Michael Serra