Identify the inscribed angles and arcs
theorem;
Use the relationship among the chords,
arcs, central angles and inscribed angles
of a circle in finding their measures;
Value accumulated knowledge as means
of new understanding.
Objective
s
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Inscribed Angles and Arcs in Circles, Slides of Mathematical Modeling and Simulation
A comprehensive guide on identifying inscribed angles and their corresponding arcs in a circle. It includes theorems, examples, and practice problems to help understand the relationship between chords, arcs, central angles, and inscribed angles. The document also covers concepts such as congruent inscribed angles and supplementary opposite angles in an inscribed quadrilateral.
Typology: Slides
2022/2023
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Identify the inscribed angles and arcs theorem; Use the relationship among the chords, arcs, central angles and inscribed angles of a circle in finding their measures; Value accumulated knowledge as means of new understanding.
Objective
s
Erica designed a pendant. It is a regular hexagon set in a circle. Suppose the opposite vertices are connected by line segments and meet at the center of the circle. What is the measure of each angle formed at the center? Answer: 60 degrees
Theorem 1. The measure of the inscribed angle is equal to one-half of its intercepted arc (or the measure of the intercepted arc is twice the measure of the inscribed angle). 47º 94º
Theorem 1. The measure of the inscribed angle is equal to one-half of its intercepted arc (or the measure of the intercepted arc is twice the measure of the inscribed angle). 43º
LET’S PRACTICE… 40º 180 º 100 º
LET’S PRACTICE…
50º 60º 70º
Theorem 2. If two inscribed angles of a circle intercept the same arc, then the angles are congruent.
Theorem 2. If two inscribed angles of a circle intercept the same arc, then the angles are congruent. and intercept Since and intercept the same arc, then two angles ( and ) are congruent.
Theorem 3. If an inscribed angle intercepts a diameter or semicircle, then the angle is a right angle.
LET’S PRACTICE… 90º 55º 35º
Check your
understanding
INSCRIBE, INTERCEPT, THEN MEASURE
=
= = (^) = =