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4.3a: Central/Inscribed Angles in Circles. GSE’s. Primary. p. 452 -458.

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### 4.3a: Central/Inscribed Angles in Circles

GSE’s

Primary

p. 452 -458

M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios(sine, cosine, tangent) within mathematics or across disciplines or contexts (e.g., Pythagorean Theorem, Triangle Inequality Theorem).

Central Angle: an angle whose vertex is at the center of the circle

A

Circle B

Has a vertex at the center

B

C

Sum of Central Angles:

The sum of all central angles in a circle

Is 360 degrees.

A

Find m

80

B

D

Little m indicates degree measure of the arc

C

AC is a minor arc. Minor arcs are less than 180 degrees. They use the

the two endpoints.

ADC is a major arc. Major arc are greater than 180 degrees. They use three letters, the endpoints and a point in-between them.

Major Concept: Degree measures of arcs are the same as its central angles

What is the mFY?

What is the mFRY?

Circle P has a diameter added to its figure every step

so all central angles are congruent.

What is the sum of the measures of 3 central angles after

the 5th step? Explain in words how you know.

Step 2

Step 1

Step 3

An angle with a vertex ON the circle and made up of 2 chords

Inscribed Angle:

Is the inscribed angle

The arc formed by connecting the two endpoints

of the inscribed angle

Intercepted Arc:

Major Concept:

Inscribed angles degree measures are half the degree measure of

their intercepted arc

Ex

What is

What is the mBG

What is the mGCB?

Important Fact: If a quadrilateral is inscribed in a circle, then the opposite angles

are SUPPLEMENTARY

What angles are supplementary

Example:

Circle C,

Find the degree measure

of all angles and arcs

Concentric Circles- circles with the same center, but different Radii

What is an example you can think of outside of geometry?

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