Basic Geometry 8.3 and 8.4 – Similar Polygons and Triangles - NOTES 2/4/13 8.3 – Similar Polygons Congruent Angles: ∠_____ ≅ ∠_____ ∠_____ ≅ ∠_____ ∠_____ ≅ ∠_____ ∠_____ ≅ ∠_____ ∠_____ ≅ ∠_____ Statement of Proportionality : side side Are they proportional? Check: PQ WX RS YZ QR XY SP ZW Similarity Statement ________________ ~ ________________ Parallelogram Top and bottom side are congruent Left and right side are congruent Top and bottom side are parallel Left and right side are parallel Remember: Alternate Interior Angles Alternate Exterior Angles Consecutive Interior Angles Corresponding Angles
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Basic Geometry 8.3 and 8.4 – Similar Polygons and Triangles - NOTES 2/4/13
Basic Geometry 8.3 and 8.4 – Similar Polygons and Triangles - NOTES 2/4/13 In the diagram at the right, RTSU ~ LMNO. 6. Find the scale factor of RTSU to LMNO 7. Find the scale factor of LMNO to RSTU. 8. Find the length of NO. 9. Find the measure of ∠U. 10. Find the perimeter of LMNO. 11. Find the ratio of the perimeter of RSTU to the perimeter of LMNO. PQRS ~ JKLM 19. Find the scale factor of PQRS to JKLM. 20. Find the scale factor of JKLM to PQRS. 21. Find the value of w, x, and y. 22. Find the perimeter of each polygon. 23. Find the ratio of the perimeter of PQRS to the perimeter of JKLM.
Basic Geometry 8.3 and 8.4 – Similar Polygons and Triangles - NOTES 2/4/13 The two polygons are similar. Find the values of x and y.
Basic Geometry 8.3 and 8.4 – Similar Polygons and Triangles - NOTES 2/4/13
8.4 – Similar Triangles
Solution a) b) c)
Solution 6. 7.
Use the diagram to complete the following 12. ∆PQR ~ ∆______
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14.
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16. y = ________
17. x = _________
RPQRPQ
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Basic Geometry 8.3 and 8.4 – Similar Polygons and Triangles - NOTES 2/4/13 The triangles are similar. Find the value of the variable. You are given that ABCD is a trapezoid, AB = 8, AE = 6, EC = 15, and DE = 10. 33. ∆ABE ~ ∆______ 34. 35. 36. 37. x = _______ 38. y = ______