11.3 Inscribed angles By: Mauro and Pato.

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Presentation transcript:

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 m<ADB = ½ mAB A 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