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.

 
 
 

gsp file


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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