4.3a: Angles and Arcsp. 452 -458

PrimaryM(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).

GSE’s

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

A

B

C

ABCCircle B

Has a vertex at the ________

Sum of Central Angles:

A

B

C

80

Find m ADC

D

Little m indicates ________ measure of the arc

AC is a ___________. Minor arcs are ________ than 180 degrees. They use the the two endpoints.

ADC is a ____________. Major arc are ___________ 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 _________________

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 1Step 2

Step 3

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

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

In Circle P

PAB

m

m )5

ABC m )4

AB m )3

BC m 2)

2m 1)

measure.each Find .ACdiameter with 1401

Arc Length:

Would we have enough info to find the circumference?

What would be needed?

Lets assume the radius of the circle is 4 inches.

Can we find the circumference now?

What if we just want to know the distance of the circumference from A to C?

What would make sense as an approach to find the length?

Find the length of BC

Find the length of CFB

What relationship should they have for this problem?

What is mCFB ?

In circle F, m EFD = 4x+6, m DFB = 2x + 20. Find mAB

NECAP Released Item 2009

Inscribed Angle: An angle with a vertex ______ the circle and made up of 2 chords

ABC Is the inscribed angle

Intercepted Arc: The arc formed by _____________________________________ of the inscribed angle

Major Concept:

Inscribed angles degree measures are ______________________ measure of their intercepted arc

Ex

What is ACBm

What is the mBG

What is the mGCB?

Major Concept: If 2 different inscribed angles intercept the same arc, thenthe angles are __________________

AGBm and

ACBm

find

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

What angles are supplementary

Example:Circle C,

Tm and Qm Find

110Rm and 28

Sm

Find the degree measure of all angles and arcs