Triangles are not the only figures that can be inscribed in a circle It is also possible to inscribe other figures such as squares The process for inscribing a square in a circle uses previously learned skills ID: 318878
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IntroductionTriangles are not the only figures that can be inscribed in a circle. It is also possible to inscribe other figures, such as squares. The process for inscribing a square in a circle uses previously learned skills, including constructing perpendicular bisectors.
1
1.3.2: Constructing Squares Inscribed in CirclesSlide2
Key ConceptsA square is a four-sided regular polygon.A
regular polygon is a polygon that has all sides equal and all angles equal.The measure of each of the angles of a square is 90˚.
Sides
that meet at one angle to create a 90˚ angle are perpendicular.By constructing the perpendicular bisector of a diameter of a circle, you can construct a square inscribed in a circle.
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1.3.2: Constructing Squares Inscribed in CirclesSlide3
Key Concepts, continued
3
1.3.2: Constructing Squares Inscribed in Circles
Constructing a Square Inscribed in a Circle
Using a Compass
To construct a square inscribed in a circle, first mark the location of the center point of the circle. Label the point
X
.
Construct a circle with the sharp point of the compass on the center point.
Label a point on the circle point
A.Use a straightedge to connect point
A
and point X. Extend the line through the circle, creating the diameter of the circle. Label the second point of intersection
C
.(
continued
)Slide4
Key Concepts, continued
4
1.3.2: Constructing Squares Inscribed in Circles
Construct the perpendicular bisector of by putting the sharp point of your compass on endpoint
A
. Open the compass wider than half the distance of . Make a large arc intersecting . Without changing your compass setting, put the sharp point of the compass on endpoint
C. Make a second large arc. Use your straightedge to connect the points of intersection of the arcs.
Extend the bisector so it intersects the circle in two places. Label the points of intersection
B
and D
.
(
continued)Slide5
Key Concepts, continued
5
1.3.2: Constructing Squares Inscribed in Circles
Use a straightedge to connect points
A
and
B, B
and C,
C
and D, and
A
and D.
Do not erase any of your markings.
Quadrilateral ABCD
is a square inscribed in circle X.Slide6
Common Errors/Misconceptionsinappropriately changing the compass settingattempting to measure lengths and angles with rulers and protractors
not creating large enough arcs to find the points of intersection
not
extending segments long enough to find the vertices of the square
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1.3.2: Constructing Squares Inscribed in CirclesSlide7
Guided PracticeExample 1Construct square ABCD inscribed in circle O.
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1.3.2: Constructing Squares Inscribed in CirclesSlide8
Guided Practice: Example 1, continuedConstruct circle O
.
8
1.3.2: Constructing Squares Inscribed in Circles
Mark the location of the center point of the circle, and label the point
O. Construct a circle with the sharp point of the compass on thecenter point.Slide9
Guided Practice: Example 1, continuedLabel a point on the circle point A
.
9
1.3.2: Constructing Squares Inscribed in CirclesSlide10
Guided Practice: Example 1, continuedConstruct the diameter of the circle.
Use a straightedge to connect point
A
and point O.
Extend the line
through the circle,
creating the diameter of the circle. Label
the second point
of intersection C.
10
1.3.2: Constructing Squares Inscribed in CirclesSlide11
Guided Practice: Example 1, continuedConstruct the perpendicular bisector of .Extend the bisector
so it intersects the circle
in two places.
Label the points of intersection B and D.
11
1.3.2: Constructing Squares Inscribed in CirclesSlide12
Guided Practice: Example 1, continuedConstruct the sides of the square.Use a straightedge to connect points
A and B, B and C
,
C and D, and A and D, as shown on the next slide. Do not erase any of your markings.
12
1.3.2: Constructing Squares Inscribed in CirclesSlide13
Guided Practice: Example 1, continuedQuadrilateral ABCD is a square inscribed in circle
O.
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1.3.2: Constructing Squares Inscribed in Circles
✔Slide14
Guided Practice: Example 1, continued14
1.3.2: Constructing Squares Inscribed in CirclesSlide15
Guided PracticeExample 3Construct square JKLM inscribed in circle Q
with the radius equal to one-half the length of .
15
1.3.2: Constructing Squares Inscribed in CirclesSlide16
Guided Practice: Example 3, continuedConstruct circle Q
. Mark the location of the center point of the circle, and
label
the point Q. Bisect the length of . Label the midpoint of the segment as point P, as shown on the next slide.
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1.3.2: Constructing Squares Inscribed in CirclesSlide17
Guided Practice: Example 3, continued
171.3.2: Constructing Squares Inscribed in CirclesSlide18
Guided Practice: Example 3, continuedNext, set the opening of
the compass equal to the length of
. Construct a circle with the sharp point
of the compass
on the center point,
Q.181.3.2: Constructing Squares Inscribed in CirclesSlide19
Guided Practice: Example 3, continuedLabel a point on the circle point J
.
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1.3.2: Constructing Squares Inscribed in CirclesSlide20
Guided Practice: Example 3, continuedConstruct the diameter of the circle.Use a straightedge
to connect point J
and point Q. Extend the line through the circle,
creating the diameter
of the circle. Label the
second point of intersection L.
20
1.3.2: Constructing Squares Inscribed in CirclesSlide21
Guided Practice: Example 3, continuedConstruct the perpendicular bisector of
.Extend the bisector
so
it intersects the circle in two places.
Label the points of intersection K
and M.
211.3.2: Constructing Squares Inscribed in CirclesSlide22
Guided Practice: Example 3, continuedConstruct the sides of the square.Use a straightedge to connect points
J and K, K and
L
, L and M, and M and J, as shown on the next slide.
Do not erase any of your markings.
22
1.3.2: Constructing Squares Inscribed in CirclesSlide23
Guided Practice: Example 3, continuedQuadrilateral JKLM is a square inscribed in circle
Q.
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1.3.2: Constructing Squares Inscribed in Circles
✔Slide24
Guided Practice: Example 3, continued24
1.3.2: Constructing Squares Inscribed in Circles