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Inscribed Angles
Lesson 9.5
Geometry Honors
Objective: Student will be able to solve
problems involving inscribed angles and
angles formed by chords and tangents.
Page 349
Lesson Focus
The purpose of this lesson is to study angles whose vertices
are on a circle. The sides of these angles pass through the
circle and cut off arcs. The measure of the angles are related
to the measures of the arcs.
Basic Terms
Inscribed Angle
An angle whose vertex is on a circle and whose sides contain
chords of the circle.
Intercepted Arc
An arc on the interior of an inscribed angle.
Basic Terms
Theorem 9-7
The measure of an inscribed angle is half the measure of its
intercepted arc.
Corollary 1
If two inscribed angles intercept the same arc, then the angles
are congruent.
Corollary 2
An angle inscribed in a semicircle is a right angle.
Corollary 3
If a quadrilateral is inscribed in a circle, then its opposite
angles are supplementary.
Theorem 9-8
The measure of an angle formed by a chord and a tangent is
equal to half the measure of the intercepted arc.
130
Problem Solving
It is important to realize that that problem solving is a creative
process that may take a great deal of time and effort.
Some challenging problems may require the student to work
on them over a period of several days.
Written exercises
Problem Set Classroom Exercises, p.353: # 4 – 9.
Written Exercises, p. 354: #1 – 9, 19 – 21.
Homework Exercises
Problem Set 9.5B: Handout