Download With your partner…

Inscribed and Circumscribed
Polygons
Inscribed
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If all of the vertices
of a polygon lie on
the circle, then the
polygon is inscribed
Circumscribed
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We can also describe this inscribed
quadrilateral as a circle circumscribed about
the quadrilateral
With your partner…
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

Sketch another large circle with your
compass.
Note where the center of the circle
is located when you’re sketching the
circle, and draw the diameter of the
circle.
Sketch a triangle such that the
vertices of the triangle lie on the
circle, making sure that the diameter
.

is one of the sides of the triangle
Measure each angle in the triangle
and make a note of them.
?

When you sketched the triangle with the
diameter being one side of the triangle, what
did you find the vertex to be?
There is a theorem that
describes this relationship…
Wherever you place the vertex with the right
angle, the hypotenuse must be the diameter.
Why do you think this is???
B
C
D
O
There is a theorem that
describes this relationship…
Let’s try and use this
theorem!
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

Solve for x
15x = 900
x=6
With your partner…
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Sketch a large circle
with your compass
Sketch a quadrilateral
such that every vertex
lies on the circle.
Label the vertices with
any letters.
With your protractor,
measure the opposite
angles, and list them.
When measuring the
opposite angles, what did
you find them to be?
There is a theorem that
states this special property
Theorem 10.11
A quadrilateral can
be inscribed in a
circle if and only if
its opposite angles
are supplementary.
Therefore,
mC  mE  180
&
mF  mD  180
Let’s try using Theorem
10.11

Find the value of each variable.