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Unit: Circles pt 1 Note Taking Guide: Lesson 2: Tangents and Similar Triangles Tangents and Similar Triangles Concentric Circles Externally Tangent Circles Internally Tangent Circles Common Internal Tangents Common External Tangents Unit: Circles pt 1 Internally Tangent Circles: Common External Tangents: Common Internal Tangents: Note Taking Guide: Lesson 2: Tangents and Similar Triangles Externally Tangent Circles: Unit: Circles pt 1 Note Taking Guide: Lesson 2: Tangents and Similar Triangles Tangent Theorem #2: If two segments from the same exterior point are tangent to a circle, then they are congruent. “Party Hat” rule! 1. x __________ 2. x __________ 3. x __________ 4. NP __________ Triangles are similar if they have the same shape, but not necessarily the same size. Properties of similar triangles: corresponding angles are the same corresponding sides are in proportion We can prove triangles are similar by: Angle-Angle (two angles congruent to two angles of another triangle) Side-Side-Side (all three sides in proportion to all three sides of another triangle) Side-Angle-Side (two proportional sides with congruent angle in between) Unit: Circles pt 1 Note Taking Guide: Lesson 2: Tangents and Similar Triangles Your Turn: The diameter of a circle is given. Find the radius. 1.__________ 1. d 17 in 2. d 18cm. 2.__________ The radius of a circle is given. Find the diameter. 3.__________ 3. r 4. r 8.3 ft. 23 cm. 4.__________ Using the diagram, name the following using the correct notation. 5.__________ Center 6.__________ Chord 7.__________ Diameter 8.__________ Radius 9.__________ Secant 10._________ Common internal tangent 11._________ Common external tangent 12._________ M P F T C J A G L Point of tangency B D E Give the number of common tangents that could be drawn in each diagram. 13._________ 14._________ 15._________ 16._________ 13. 14. 15. 16. Unit: Circles pt 1 Note Taking Guide: Lesson 2: Tangents and Similar Triangles For each figure below, identify the number of points of intersection and the number of common internal and external tangents: Points of intersection # Common internal tangents # Common external tangents 17. ____________ _______________ ______________ 18. ____________ _______________ ______________ 19. Make a rule! Diagram