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Geometry worksheet in which students develop and apply the theorem relating the measure of an inscribed angle to the measure of its intercepted arc.
Geometry worksheet to help students apply theorems relating the measures of inscribed angles and angles at the intersections of chords and tangents to the measures of their intercepted arcs.

Activity 3.8​

Assignment 3.9

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​Assignment 10.11

​Measure of Inscribed Angles

 
Objectives
Develop and apply a theorem relating the measure of an inscribed angle to the measure of its intercepted arc.
 
Apply a theorem relating the measure of an angle with its vertex at the intersection of a chord and a tangent to the measure of its intercepted arc.

About Geometry Worksheet Assignment 10.11:                 

 

Assignment 10.11 is an introduction to the theorem about the measures of inscribed angles and the measures of their intercepted arcs.

 

Prerequisite Skills:  Measure angles with a protractor (Assignment 2.5).  Find the measure of arcs by measuring central angles (Assignment 10.8). Identify inscribed angles and their intercepted arcs (Assignment 10.10).

 

Theorems:  The measure of an inscribed angle is one-half the measure of its intercepted arc.

                           (The measure of an arc subtending an inscribed angle is twice the measure of the angle.)

 

                           The measure of an angle at the intersection of a tangent and a chord is one-half the measure of its intercepted arc.  

                           (The measure of an arc subtending the angle at the intersection of a tangent and a chord is twice the measure of the angle.)

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