unit 8.3  property of angles in circles
what we need to know
 Radius, diameter and chords: definitions and differences among them.
 Angles are named after the letters from which they originate.
 The letter in the middle of an angle's name is where the lines meet. These lines originate at each of the other 2 letters.
 For example, angle AOB is at O, and this is the place where A and B meet (A and B meet at O).
 A straight line has an angle of 180 degrees. Think of the diameter... The diameter cuts the circle in half, thereby "cutting" the 360 degrees of the circle in half (180 degrees).
 Angles are named after the letters from which they originate.
 The letter in the middle of an angle's name is where the lines meet. These lines originate at each of the other 2 letters.
 For example, angle AOB is at O, and this is the place where A and B meet (A and B meet at O).
 A straight line has an angle of 180 degrees. Think of the diameter... The diameter cuts the circle in half, thereby "cutting" the 360 degrees of the circle in half (180 degrees).
what we did in class
9_unit_8.3_class_notes__activity.pdf  
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extra information
In this part of the unit, we will be dealing with the concepts of MAJOR and MINOR ARCS. Take a look at the following definitions:
The concept of the MINOR ARC is important because, in this part of the unit, all angles we will be dealing with WILL ORIGINATE from the minor arc. The word that you may see on your textbook, and perhaps on your P.A.T., is the word SUBTENDED, which means "TO ORIGINATE FROM".
MINOR ARC = The PARENTS (where the angles originate, or come, from)
Keeping the concept of the MINOR ARC in mind, let's us take a look at the different properties of angles in circles. Before we do, however, we need to get comfortably acquainted with two definitions:
MINOR ARC = The PARENTS (where the angles originate, or come, from)
Keeping the concept of the MINOR ARC in mind, let's us take a look at the different properties of angles in circles. Before we do, however, we need to get comfortably acquainted with two definitions:
Definition of a Central ANgle
The angle formed by joining the endpoints of an arc to the centre of the circle is called a CENTRAL ANGLE.
As you can see, the "arms" of central angles are radiii (singular = radius).
definition of an inscribed angle
The angle formed by joining the endpoints of an arc to a point on the ACTUAL CIRCLE is called an INSCRIBED ANGLE.
central angle and Inscribed angle property
This property says that in a circle, the measure of a CENTRAL ANGLE is TWICE the measure of AN INSCRIBED ONLY. HOWEVER.... This is only possible WHEN AND IF THESE ANGLES ARE SUBTENDED (COME FROM) BY THE SAME MINOR ARC (that is, the central and the inscribed angle come from the same "parents" and therefore are "siblings".
inscribed angles property
This property says that all INSCRIBED ANGLES subtended by (COMING FROM) the same minor arc ARE EQUAL. To be able to see if angles come from the same arc. always start at the inscribed angle and TRACE BACK to see where it comes from.
angles in a semicircle property
 A diameter, which goes through the center of the circle, cuts the circle into 2 SEMICIRCLES. That is, the two arcs formed by the endpoints of a diameter are semicircles.
 This means that the central angle formed by the diameter is 180 degrees. This also means that the INSCRIBED ANGLE originated at each end of the DIAMETER is always a RIGHT ANGLE (90 degrees).
 This means that the central angle formed by the diameter is 180 degrees. This also means that the INSCRIBED ANGLE originated at each end of the DIAMETER is always a RIGHT ANGLE (90 degrees).
examples of central and inscribed angles property applications
EXAMPLES OF ANGLES IN A semicircle property application
videos that may help
interactive online activities
worksheets






review  workbook
workbook__unit_8.3.pdf  
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