Day five:
The inscreibed angle of an intercepted
angle
by Nami Youn
Objective
To discover the relationship of the central angle and the inscribed angle
of an intercepted arc
To understand the properties of an arc and the inscribed angle of the intercepted
arc
1. The relationship of the central
angle and inscribed angle of an intercepted arc
Property 1 : In a circle, the measure
of an inscribed angle is equal to half the measure of the central angle
with the same intercepted arc.
Property 2 : If a triangle is inscribed
in a circle so that one side of the triangle is a diameter of the circle,
then the angle opposite that side is a right angle
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2. The
properties of an arc and the angle at circumference of an arc
Property 1 : In a circle, the angle
at circumference of the arcs with the same measure are all the same.
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Property 2 : In a circle, two inscribed
angles with the same intercepted arc are congruent.
Property 3 : The angle at circumference
of an arc is proportional to the measure of the arc.
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