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Geometry
Portfolio Activity: Criss-Crossing the Circle
Through the technique of paper folding, you will discover several properties of
circles. For each part, you will need to cut out a circle from the template sheet (or
draw your own). Trace or highlight any folds making segments or angles. Provide
a sketch of your circle with all of the steps completed. Glue your completed circle to
the space below each problem (“C” needs to be glued down before it is completed).
A. Chords of a Circle
Part 1 – Diameters
Instructions:
1. Cut out a circle from the template sheet.
2. Find the center of the circle by folding it to create
two diameters.
3. Create several chords parallel to one of the
diameters in step 2.
Sketch
Properties:
 Which chord is the longest chord? ___Diameter____
 Complete the following statement:
“as the length of the chord increases, the distance from
the center _decreases_.”
Part 2 – Congruent Chords
Instructions:
1. Cut out a circle from the template sheet.
2. Create three chords of the same length on the
circle.
3. Fold each of these chords with a perpendicular
bisector to find the center of the circle.
4. Measure the distance from each chord to the center
of the circle.
Sketch
Properties:
 Complete the following statements:
1. “If chords are congruent, then they must be
_equidistant__ from the center of the circle.”
2. “If two chords are equidistant from the center of a circle,
then they must be __congruent__.”
3. “The perpendicular bisector of a chord goes through the
____center____ of a circle.”
4. “The perpendicular to a chord through the __center___ of
a circle ___bisects___ the chord.”
B. Angles of a Circle
Sketch
Part 1 – Inscribed Angles
Instructions:
1. Cut out a circle from the template sheet.
2. Fold two chords on the circle to create an inscribed
angle.
3. Create another inscribed angle that opens to the
same arc as the inscribed angle in step 2.
4. Measure the inscribed angles created.
Properties:
 Complete the following statement:
“The measure of inscribed angles opening onto the same
arc or chord are __the same___.”
Sketch
Part 2 – Inscribed & Central Angles
Instructions:
1. Cut out a circle from the template sheet.
2. Fold two chords on the circle to create an inscribed
angle.
3. Find the center of the circle.
4. Find the center of the circle by folding along two
diameters that each share an endpoint with the arc
intercepted by the inscribed angle. Trace only the
radii from the center to the intercepted arc. (a
sketch has been provided to the right to help with
this construction.)
5. Measure the inscribed angle and the central angle.
Properties:
 Complete the following statement:
“If a central angle and an inscribed angle open onto the
same arc, then the ratio of the measure of the central
angle to the inscribed angle is __2__ : __1__.”
C. Tangents to a Circle
Sketch
Part 1 – Tangents
Instructions:
1. Cut out a circle from the template sheet.
2. Fold the circle to create any two diameters. Trace
one radius from each diameter.
3. Glue this circle in the space below.
4. Draw two tangents to the circle intersecting the
two radii from step 2.
5. Mark the points where the tangents intersect the
circle and where the tangents intersect each other.
6. Measure the lengths of tangent segments from
their point of intersection to the points of tangency.
7. Measure the angle made by the tangent segments
and the radii of the circle.
Properties:
 Complete the following statements:
1. “The tangent segments from a common point outside a
circle are __congruent__ in length.”
2. “An angle formed by a tangent and a radius of the same
circle intersecting at the point of tangency measures
__90˚__ degrees.”