# MM2G3 Students will understand properties of circles. MM2G4

MM2G3 Students will understand properties of circles. MM2G4 Students will find and compare the measures of spheres. Review for Unit Test Friday, February 28, 2020 Essential Question: How do we use the theorems of circles? M2 Unit 3: Day 13 MM2G3 b Understand and use properties of central, inscribed, and related angles. MM2G3 d Justify measurements and relationships in circles and geometric and algebraic properties. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. MM2G3 Students will understand properties of circles. MM2G4 Students will find and compare the measures of a sphere.

Arcs and Chords arc of the chord chord -Two minor arcs are if and only if their corresponding chords are - Inscribed polygons has each vertex on the circle - If the diameter of a circle is perpendicular to a chord, it bisects the cord & the arc 11 -Two chords are iff they are equidistant from the center. .

MM2G3 b Understand and use properties of central, inscribed, and related angles. MM2G3 d Justify measurements and relationships in circles and geometric and algebraic properties. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. 11 MM2G3 Students will understand properties of circles. Inscribed Angles Intercepted arc

Inscribed An inscribed has its vertex on the circle Inscribed polygons have all vertices on the circle Opposite s of inscribed quadrilaterals are supplementary The measure of inscribed s = intercepted arc If an inscribed intercepts a semicircle, the m = 90 If 2 inscribed s intercept the same arc, the s are red & blue s are MM2G3 b Understand and use properties of central, inscribed, and related angles. MM2G3 d Justify measurements and relationships in circles and geometric and algebraic properties. MM2G3 Students will understand properties of circles. Tangents

Tangent lines intersect the circle at 1 pointthe point of tangency A line is tangent to the circle iff it is perpendicular the the radius drawn at that particular point If a point is outside the circle & 2 tangent segments are drawn from it, the 2 segments are congruent. .

Tangents can be internal or external MM2G3 b Understand and use properties of central, inscribed, and related angles. MM2G3 d Justify measurements and relationships in circles and geometric and algebraic properties. MM2G3 Students will understand properties of circles. Secants, Tangents & Angle Measures I A secant line intersects the circle in 2 points Intersecting at point of tangency A C B D

1 secant & 1 tangent 1 ABC = BC 2 1 BCD = BD 2 MM2G3 b Understand and use properties of central, inscribed, and related angles. MM2G3 d Justify measurements and relationships in circles and geometric and algebraic properties. MM2G3 Students will understand properties of circles. MM2G4 Students will find and compare the measures of a sphere. Secants, Tangents & Angle

Measures B 1 A C 2 D Intersection in interior of circle 2 secants: forms 2 pair of vertical angles Vertical are 1

m 1 = (mAB + mAD) 2 1 m 2 = ( mAB + mCD) 2 MM2G3 b Understand and use properties of central, inscribed, and related angles. MM2G3 d Justify measurements and relationships in circles and geometric and algebraic properties. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. Secants, Tangents & Angle Measures Intersection at exterior point Case 1 2 secants C

B P A 1 mCPD = (mCD - mAB) 2 D Case 2 1 secant & 1 tangent 1 mCPB = (mCB - mAD)

2 Case 3 2 tangents B Q P A C D B P A

1 mAPB = (mAQB - mAB) 2 MM2G3 Students will understand properties of circles. c Special Segments in a Circle If two chords intersect inside (or outside) of a circle, the products of their segments are equalab = cd 2 secants & exterior point:: a(a + x) = b(b + c) 1 tan and 1 sec & exterior point a

x b a x a b c a2 = x(x + b) = x2 + bx MM2G3 b Understand and use properties of central, inscribed, and related angles. MM2G3 d Justify measurements and relationships in circles and geometric and algebraic properties.

b d MM2G3 Students will understand properties of circles. MM2G4 Students will find and compare the measures of a sphere. MM2G3 b Understand and use properties of central, inscribed, and related angles. MM2G3 d Justify measurements and relationships in circles and geometric and algebraic properties. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. MM2G3 Students will understand properties of circles. MM2G4 Students will find and compare the measures of a sphere. MM2G3 b Understand and use properties of central, inscribed, and related angles. MM2G3 d Justify measurements and relationships in circles and geometric and algebraic properties. MM2G4 a Use and apply the area and volume of a sphere.

MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. MM2G3 Students will understand properties of circles. MM2G4 Students will find and compare the measures of a sphere. MM2G3 b Understand and use properties of central, inscribed, and related angles. MM2G3 d Justify measurements and relationships in circles and geometric and algebraic properties. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. MM2G3 Students will understand properties of circles. MM2G4 Students will find and compare the measures of a sphere. MM2G3 b Understand and use properties of central, inscribed, and related angles. MM2G3 d Justify measurements and relationships in circles and geometric and algebraic properties. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

MM2G3 Students will understand properties of circles. MM2G4 Students will find and compare the measures of a sphere. MM2G3 b Understand and use properties of central, inscribed, and related angles. MM2G3 d Justify measurements and relationships in circles and geometric and algebraic properties. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. MM2G3 Students will understand properties of circles. MM2G4 Students will find and compare the measures of a sphere. MM2G3 b Understand and use properties of central, inscribed, and related angles. MM2G3 d Justify measurements and relationships in circles and geometric and algebraic properties. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. MM2G3 Students will understand properties of circles. MM2G4 Students will find and compare the measures of a sphere.

MM2G3 b Understand and use properties of central, inscribed, and related angles. MM2G3 d Justify measurements and relationships in circles and geometric and algebraic properties. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. MM2G3 Students will understand properties of circles. MM2G4 Students will find and compare the measures of a sphere. MM2G3 b Understand and use properties of central, inscribed, and related angles. MM2G3 d Justify measurements and relationships in circles and geometric and algebraic properties. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. MM2G3 Students will understand properties of circles. MM2G4 Students will find and compare the measures of a sphere. MM2G3 b Understand and use properties of central, inscribed, and related angles.

MM2G3 d Justify measurements and relationships in circles and geometric and algebraic properties. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere. MM2G3 Students will understand properties of circles. MM2G4 Students will find and compare the measures of a sphere. Homework: Finish Unit 3 Study Guide (Unit 3 Test is tomorrow) MM2G3 b Understand and use properties of central, inscribed, and related angles. MM2G3 d Justify measurements and relationships in circles and geometric and algebraic properties. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

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