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.