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

ZWSimilarity 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

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 ~ ∆______

13.

14.

15.

16. y = ________

17. x = _________

RPQRPQ

12

20

18

20

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 = ______

BEAEAB

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