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