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

1) Equilateral Triangle2) Square3) Hexagon

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?

How did you do?pg. 100 #’s

Proportions in TrianglesToolkit #8.5

Today’s Goal(s):1. To use the Side-Splitter

Theorem.2. To us the Triangle-Angle

Bisector Theorem.

Side-Splitter TheoremFor a triangle…

Side-Splitter TheoremFor three parallel lines…

If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.

d

c

b

a

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.

DC

AD

CB

AB

Ex.1: Using the Side-Splitter Theorem Solve for x.

a.)

b.)

Ex.2: Solve for x and y.

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

Ex.3: Using the Triangle-Angle Bisector Thm.

Find the value of x.

a.)

b.)

Perimeters and Areas of Similar Figures

Toolkit #8.6

Today’s Goal(s):1. To find the perimeters and

areas of similar figures.

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.

Sim. Ratio = _____

Per. Ratio = _____

Area Ratio = _____

The ratio of their PERIMETERS is a : b. The ratio of their AREAS is a2 : b2

P = 24 ft

P = ?

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 = ?

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 = 5

2

10

4or

25

4

5

22

2

or

A

5.27

25

4

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)

Ex.1: Finding Ratios in Similar FiguresFind the ratio of the perimeters and areas of each pair of similar figures.

a.) b) Two similar polygons have corresponding sides in the ratio of 5:7.

EOC REVIEW #7Tuesday – March 25, 2008

1. If ABCD is a rhombus and m<ABC = 60, what is the measure of <1 and <2?

2. ABCD is a trapezoid. If m<2 = 5x – 20 and m<3 = 3x, find x, y, and m<2 and m<3.

W.B. p. 98

10. 11.

Try this one…