CHAPTER 10 CIRCLE GEOMETRY - WordPress.com · CIRCLE GEOMETRY PG 374 NOTE: You Need your GEOMETRY...
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May 4, 2020 CHAPTER 10 CIRCLE GEOMETRY PG 374 NOTE: You Need your GEOMETRY SET for this unit!
Transcript of CHAPTER 10 CIRCLE GEOMETRY - WordPress.com · CIRCLE GEOMETRY PG 374 NOTE: You Need your GEOMETRY...
May 4, 2020
CHAPTER 10
CIRCLE GEOMETRY
PG 374
NOTE: You Need your GEOMETRY SET for this unit!
May 4, 2020
May 4, 2020
Quick Review for Chapter 10Naming Angles Pythagorean Theorem
SR
K
L
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Applying the Pythagorean Theorem
#1) #2) #3)
3.5
7.2
x
Find x in each of the following questions
12.75m
8.2m
x x 14.4cm
5.7cm
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Subtendhttps://www.mathsisfun.com/definitions/subtend.html
Subtend -The side or arc opposite of the angle
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Section 10.1Exploring Angles in a CircleINSCRIBED ANGLE PROPERTY:The inscribed angles SUBTENDED by the same arc are congruent(equal).
CENTRAL/INSCRIBED ANGLE PROPERTY:The measure of the central angle is equal to TWICE the measure of the inscribed angle. OrThe measure of the inscribed angle is equal to 1/2 the measure of the central angle.
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(1) Determining Angles in a Circle
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Pre-Activity:
STEPS:1) On a blank sheet of paper draw a circle and label its center C.2) Draw a diameter and label it AB3) What is the measure of the angle ACB?4) Now place a point E on the circumference of the circle and attach EA and EB to create an inscribed angle AEB.5) What is the measure of the angle AEB?6) What do you notice?
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SOLUTION
CA B
E
You should notice that angle AEB is half of the angle ACB since they subtend the same are AB, and angle AEB is an inscribed angle and ACB is a central angle both subtending the same arc AB.
FURTHERMORE:Triangle AEB is a right triangle!
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(2) Using Angles to Recognize Relationships
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(3) Using Angles to SOLVE PROBLEMSA flashlight has a field of view of 25, and a camera of 50. How can you position the camera and the flashlight so that the camera can capture the same area as the flashlight illuminates?
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Solution is on the next page, however, try to tackle this on your own first:
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Solution Steps:
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Let's look at central angles that are greater than 180 degrees, and inscribed angles subtending the same arc.
Also let's look at angles within isosceles and equilateral triangles.
Enrichment!!
Supplementary angles are two angles whose sum is 180 degrees.
Complementary angles are two angles whose sum is 90 degrees.
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Additional resources to support with Geometry
Additional resources: for numbers/patterns/shape and space/geometry
www.learnalberta.ca
