4.3a: Angles and Arcs p. 452 -458 Primary M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses.

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Presentation transcript:

4.3a: Angles and Arcs p Primary 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). GSE’s

Central Angle: an angle whose vertex is at the center of the circle A B C Circle B Has a vertex at the ________ Sum of Central Angles: A B C 80 Find m 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 5 th step? Explain in words how you know. Step 1 Step 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

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 Find mAB

NECAP Released Item 2009

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

What is the mBG What is the mGCB?

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

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

Example: Circle C,

Find the degree measure of all angles and arcs