Download 11.3 Inscribed angles - asfg-grade-9

11.3 Inscribed angles
By: Mauro and Pato
Objectives:
• Define Inscribe angle, intercepted arc, inscribed
and circumscribed.
• Be able to know the theorems “Measure of an
Inscribed Angle”, Theorem 10.9 and theorems
about inscribed polygons (theorem 10.10 and
10.11).
• Be able to apply this knowledge on any kind of
problems related to this topic.
• Laugh the 45 minutes of class and have a good
time.
Geometry Background:
• Circles: a round plane figure whose boundary
(the circumference) consists of points
equidistant from a fixed point (the center).
• Polygons: a plane figure with at least three
straight sides and angles, and typically five or
more.
• Supplementary Angles: either of two angles
whose sum is 180º.
You will learn:
• What is an inscribed angle.
• What is an intercepted arc.
• Four different theorems and how to apply
them.
Inscribed Angle
Measure of an Inscribed Angle
• If an angle is inscribed in a circle, then its
measure is half its measure is half the
measure of its intercepted arc
A
• m<ADB = ½ mAB
D
B
example
Theorem 10.9
• If two inscribed angles of a circle intercept the
same arc, then the angles are congruent
A
B
C
D
example
Remember?
• Circumscribed: (draw a figure around another)
touching the figure by touching its sides but
not cutting it.
• Inscribed: draw a figure within another so that
their boundaries touch but do not intersect.
Theorem 10.10
• If a right triangle is inscribed in a circle, then the hypotenuse is a diameter
of the circle. Conversely, if one side of an inscribed triangle is a diameter
of the circle, then the triangle is a right triangle and the angle opposite the
diameter is the right angle.
C
A
B
example
Theorem 10.11
• A quadrilateral can be inscribed in a circle if
and only if its opposite angles are
supplementary.
E
F
C
D
G
example