Inscribed Angles with Algebra
Presentation
•
Mathematics
•
9th - 12th Grade
•
Hard
Joseph Anderson
FREE Resource
5 Slides • 6 Questions
1
Learning : You should be able to use the relationships of inscribed angles and their intercepted arcs to determine missing arc and angle measures as well as solve algebraic expressions.
2
Match
Let's review our vocabulary first!
Match the vocabulary words to their definitions.
an unbroken part of a circle
formed when two straight lines or rays meet at a common endpoint
an angle whose vertex is ON the circle
an arc that is encased on either side by two different segments whose endpoints are also endpoints of an inscribed angle
arc
angle
inscribed angle
intercepted arc
arc
angle
inscribed angle
intercepted arc
3
Labeling
Label each of the highlighted parts of the circle with the correct vocabulary word.
arc
intercepted arc
angle
inscribed angle
4
Let's see if you can determine the relationship between inscribed angles and their intercepted arcs.
1. Look at the following examples.
2. Jot down what you notice.
5
Open Ended
What did you notice about the inscribed angles and their intercepted arcs?
6
What have we discovered?
The measure of an inscribed angle is 1/2 its intercepted arc.
7
Open Ended
The inscribed angle being half the measure of the intercepted arc is the same as saying, "The intercepted arc is ___________ the inscribed angle".
What would you fill in the blank with?
8
Given the measure of the intercepted arc...
to find the measure of the intercepted arc, we will:
Multiply the inscribed angle by 2
Given the measure of the inscribed angle...
to find the measure of the inscribed angle, we will:
Multiply the intercepted arc by 1/2
OR
Divide the intercepted arc by 2
9
10
Math Response
Determine the measure of the missing inscribed angle.
11
Math Response
Determine the measure of the missing intercepted arc.
Learning : You should be able to use the relationships of inscribed angles and their intercepted arcs to determine missing arc and angle measures as well as solve algebraic expressions.
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