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CCGPS Analytic Geometry

CCGPS Analytic Geometry. GEOMETRY!!!. 5 Ways to Prove Triangles Congruent. SSS : All 3 sides are exactly the same SAS : 2 congruent sides and the angle in between ASA : 2 congruent angles are the side in between AAS : 2 congruent angles and a side NOT in between

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CCGPS Analytic Geometry

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  1. CCGPS Analytic Geometry GEOMETRY!!!

  2. 5 Ways to Prove Triangles Congruent • SSS: All 3 sides are exactly the same • SAS: 2 congruent sides and the angle in between • ASA: 2 congruent angles are the side in between • AAS: 2 congruent angles and a side NOT in between • HL: ONLY FOR RIGHT TRIANGLES – Hypotenuse and 1 Leg

  3. CONGRUENCE STATEMENT Order matters! Match up corresponding parts. Example: ABC  DEF

  4. Triangle Sum The 3 angles in a triangle add up and equal ______. 180

  5. Exterior Angle Theorem The 2 remote interior angles add up and equal the exterior angle Remote Angle Exterior Angle Remote Angle

  6. Isosceles Triangle • 2 congruent sides • Opposite of the congruent sides are congruent angles

  7. Rigid Motion – the shape will still be congruent after the move • Reflection • Translation • Rotation

  8. Dilate the figure by 1/2. Use the origin as the center of dilation.

  9. Dilate the figure by 2. Use (-2,0) as the origin as the center of dilation. To do this, you have to calculate the distance each point is away from the center of dilation and then multiply that distance by the dilation factor.

  10. Find the center of dilation

  11. Similar Polygons • Corresponding angles are congruent • Corresponding sides are proportional • Similarity Statement

  12. Solve for x and y. L A 5 cm S x 10 cm y 13 cm C B 24 cm T x = 26 cm y = 12 cm

  13. In similar triangles, angles are congruent and sides are proportional Find the missing angle measures. A L 53 S C B 37 T

  14. Find the perimeter of the smaller triangle. 12 cm 4 cm Perimeter = x Perimeter = 60 cm x = 20 cm

  15. 3 ways to Prove Triangles Similar • Angle-Angle (AA~) Similarity Postulate • Side-Side-Side (SSS~) Similarity Theroem • Side-Angle-Side (SAS~) Similarity Thm

  16. Determine whether the triangles are similar. If so, tell which similarity test is used and complete the statement. Yes, AA~ 68° 43° 68° 43° V NO Y 7 3 Z 5 X W U 11

  17. S 5 4 Q P 12 15 R T Prove that RST ~ PSQ 1. Two sides are proportional 2. Included angle is congruent SAS~

  18. A tree cast a shadow 18 feet long. At the same time a person who is 6 feet tall cast a shadow 4 feet long. How tall is the tree?

  19. Trig Ratios

  20. Trig Ratio What is cos R? What is sin R? What is tan R?

  21. Co-Function Relationships

  22. Co-Function Relationships Cos 64 = Sin ____ 26

  23. Find a Missing Side Solve for x. Round to the nearest tenth. x x = 17.6

  24. Find a Missing Angle Solve for . Round to the nearest tenth.   = 31.4

  25. The angle of elevation from a ship to the top of a 35 meter lighthouse on the coast measures 26.How far from the coast is the ship? Round to the nearest tenth. tan 26 = 35/x x = 71.8 m

  26. Angle Formulas to KNOW for the Test

  27. Solve for x. x

  28. Solve for x. 110 x 40

  29. Solve for x. 38 A B x D C 148

  30. solve for x A B 42 x C D

  31. solve for x. C 164 A S x 22 T

  32. A Solve for x. (Circle A) 168 x

  33. solve for x. 120 x 130

  34. Solve for x and y.

  35. Area & Circumference

  36. Find the arc length and area of the shaded sector.

  37. Formulas to KNOW for the Test - Segments

  38. Solve for x. 2 x 3x 6

  39. Solve for x. 4 x 5 10

  40. Question 18: Solve for x. x 7 9

  41. solve for x. 10 x 3 5

  42. Find the perimeter of the polygon. 9 cm 16 cm     8 cm 6 cm

  43. Volume of Solids

  44. Area of Base

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