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4.3a: Central/Inscribed Angles in Circles p. 452 -458 GSE’s 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). Central Angle: an angle whose vertex is at the center of the circle A Circle B ABC 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 ADC 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 In Circle P m1 140 with diameter AC. Find each measure. 1) m2 2) m BC 3) m AB 4) m ABC 5) mPAB In circle F, m EFD = 4x+6, m DFB = 2x + 20. Find mAB NECAP Released Item 2009 Inscribed Angle: An angle with a vertex ON the circle and made up of 2 chords ABC Is the inscribed angle Intercepted Arc: The arc formed by connecting the two endpoints of the inscribed angle Major Concept: Inscribed angles degree measures are half the degree measure of their intercepted arc Ex What is mACB What is the mBG What is the mGCB? Major Concept: If 2 different inscribed angles intercept the same arc, then the angles are congruent find mACB and mAGB Important Fact: If a quadrilateral is inscribed in a circle, then the opposite angles are SUPPLEMENTARY What angles are supplementary Example: Circle C, mS 28 and mR 110 Find mQ and mT 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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