Unit 4: Unit 4: Circles and Volume Introduction to Circles.

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Unit 4: Unit 4: Circles and Volume Introduction to Circles

Instructions You will view the PowerPoint independently Write down the vocabulary and Illustrations for each term Check for understanding with the Practice Questions Set A – E (Make sure these examples are in your composition notebook) See me with any questions You have 20 minutes to complete!!

Circle Vocabulary

Circle – set of all points _________ from a given point called the _____ of the circle. C Symbol: equidistant center C

CHORD: A segment whose endpoints are on the circle

P DIAMETER: Distance across the circle through its center Also known as the longest chord.

P RADIUS: Distance from the center to a point on the circle

Formula Radius = ½ diameter or Diameter = 2r

D = ? r = ? D = ? Set A Guided Practice Questions Set A

Use  P to determine whether each statement is true or false. P Q R T S Set B Guided Practice Questions Set B

Secant Line: intersects the circle at exactly TWO points

a LINE that intersects the circle exactly ONE time Tangent Line: Forms a 90°angle with one radius Point of Tangency: The point where the tangent intersects the circle

Name the term that best describes the notation. Secant Radius Diameter Chord Tangent Set C Guided Practice Questions Set C

Central Angles An angle whose vertex is at the center of the circle

P A B C 3 Types of Arcs Minor Arc Major Arc Less than 180° More than 180° AB ACB To name: use 2 letters To name: use 3 letters  APB is a Central Angle

P E F D Semicircle : An Arc that equals 180° EDF To name: use 3 letters

THINGS TO KNOW AND REMEMBER ALWAYS A circle has 360 degrees A semicircle has 180 degrees Vertical Angles are CONGRUENT Linear Pairs are SUPPLEMENTARY

Formula measure Arc = measure Central Angle

m AB m ACB m AE A B C Q 96  E = = = 96° 264° 84° Find the measures. EB is a diameter. Set D Guided Practice Questions Set D

Arc Addition Postulate A B C m ABC = m AB + m BC

Tell me the measure of the following arcs. AC is a diameter. 80  100  40  140  A B C D R m DAB = m BCA = 240  260  Set E Guided Practice Questions Set E

Congruent Arcs have the same measure and MUST come from the same circle or of congruent circles. 45 A B C D 110 Arc length is proportional to “r”