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Warm Up: Draw each regular polygon and find an exterior angle and it’s interior angle.

Warm Up: Draw each regular polygon and find an exterior angle and it’s interior angle. Equilateral Triangle Square Hexagon. Review. If the measure of one exterior angle of a regular polygon is 72º, how many sides does the polygon have?

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Warm Up: Draw each regular polygon and find an exterior angle and it’s interior angle.

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  1. Warm Up: Draw each regular polygon and find an exterior angle and it’s interior angle. Equilateral Triangle Square Hexagon

  2. Review • If the measure of one exterior angle of a regular polygon is 72º, how many sides does the polygon have? • What is the measure of one of its interior angles?

  3. How did you do?pg. 100 #’s

  4. Proportions in TrianglesToolkit #8.5 Today’s Goal(s): To use the Side-Splitter Theorem. To us the Triangle-Angle Bisector Theorem.

  5. Side-Splitter TheoremFor a triangle…

  6. Side-Splitter TheoremFor three parallel lines… • If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.

  7. Triangle-Angle Bisector Theorem • If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.

  8. Ex.1:Using the Side-Splitter Theorem Solve for x. a.) b.)

  9. Ex.2: Solve for x and y.

  10. Ex.2 cont…The segments joining the sides of trapezoid RSTU are parallel to its bases.

  11. Ex.3:Using the Triangle-Angle Bisector Thm.Find the value of x. a.) b.)

  12. Perimeters and Areas of Similar FiguresToolkit #8.6 Today’s Goal(s): To find the perimeters and areas of similar figures.

  13. If the similarity ratio of two similar figures is a : b, then… • The ratio of their PERIMETERS is a : b. • The ratio of their AREAS is a2 : b2.

  14. The ratio of their PERIMETERS is a : b. • The ratio of their AREAS is a2 : b2 Sim. Ratio = _____ Per. Ratio = _____ Area Ratio = _____ P = 24 ft P = ?

  15. The ratio of their PERIMETERS is a : b. • The ratio of their AREAS is a2 : b2 Sim. Ratio = _____ Per. Ratio = _____ Area Ratio = _____ A = 4 cm2 A = ?

  16. You Try…(Use the back of your toolkit.)The area of the smaller regular pentagon is about 27.5 cm2.Find the area (A) of the larger regular pentagon. Similarity Ratio = Area Ratio =

  17. STOP and THINK!Are all regular polygons with the same number of sides similar? Yes! Why? All regular polygons are… • Equiangular(angles are congruent) • Equilateral(ratio of sides of any two regular polygons is the same)

  18. a.) Two similar polygons have corresponding sides in the ratio of 5:7. Ex.1:Finding Ratios in Similar FiguresFind the ratio of the perimeters and areas of each pair of similar figures.

  19. EOC REVIEW #7 Tuesday – March 25, 2008 • If ABCD is a rhombus and m<ABC = 60, what is the measure of <1 and <2? • ABCD is a trapezoid. If m<2 = 5x – 20 and m<3 = 3x, find x, y, and m<2 and m<3.

  20. W.B. p. 98 10. 11.

  21. Try this one…

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