Bell Work 1/28/13• 1) Write a statement of proportionality for

the picture below if ABCD ~ MNOP

• 2) Solve for x in the following proportions:

• A) B)

• 3) Simplify the ratios below:

• A) B)

2 2 3

4 5

x x 3 3 4

12 6 4

x

x

5

10

ft

in

70

4000

m

cm

Agenda• 1) Bell Work

• 2) IP Check

• 3) Review(Socrative Student ?’s)

• 4) Similar Figures(finish 8.3 notes)

• 5) Golden Ratio Activity

• 6) Identifying similar triangles

Socrative Student

• Open Socrative student on your tablets(if you do not have your tablet, notice there are 5 spaces at the bottom of your bell work sheet)

What is a ratio?• A) A comparison of two quantities in the

same units

• B) A relation in number between similar things

• C) An equation in which four quantities are shown to have equal ratios

• D) All of the above

• E) A and B

What type of mathematical operation is ratio?

• A) Multiplication

• B) Addition

• C) Subtraction

• D) Division

What is a proportion?• A) A fraction that relates two quantities

• B) A piece of pie

• C) An equation in which four quantities are shown to have equal ratios

• D) None of the above

What two things must you check to determine if figures are similar?

• A) The angles from each figure have the same name and the figures have the same number of sides

• B) The side lengths from each figure are all the same and their angles are all the same

• C) The corresponding angles are congruent and the corresponding side lengths are proportional

• D) None of the above, you can tell just by looking

Determine if the following figures are similar

• What is the similarity statement?• A) KLM ~ PRO B) KML ~ PRO• C) KLM ~ POR D) They aren’t similar

Examples

Scale Factor

• Scale Factor - The ratio of the lengths of two corresponding sides of two similar polygons.

Theorem 8.1

• If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.

KL LM MN NK KL

PQ QR RS SP PQ

Example

The “Golden Ratio”• Leonardo da Vinci, a classic “Renaissance man,” was

very interested in the relationship between math and the human body. During his apprenticeship under Andrea del Verrocchio, he was encouraged to study anatomy, dissecting countless animals and human corpses. He eventually developed what he would call the “divine proportion” or “golden ratio.”

• He used this ratio in many of his masterpieces (including The Mona Lisa). Two quantities are in the divine proportion if the sum of the two quantities divided by the larger quantity equals the larger quantity divided by the smaller.

• Mathematically, the “golden ratio” looks like this:

• The golden ratio as a number is about 1.618

a b a

b b

Golden Ratio Activity

• Does your body have the “golden ratio”?

• With a partner and a yard stick, find the following measurements, and determine what ratio you are in.

• We will see if anyone is close to exhibiting the same ratios that Da Vinci used when he painted The Mona Lisa.

• Measurements needed:

Scale Factor• Scale Factor: The ratio of the lengths of

two corresponding sides of two similar polygons

• Example: If Triangle ABC ~ Triangle DEF what is the scale factor of the triangles?

A

BC

D

EF

512

Scale Factor = 12

5

Shortcuts

• Just as when looking at triangle congruence, there are shortcuts to help us determine if triangles are *similar.

Similar Triangles

If Two angles of one triangleare congruent to two anglesin another triangle, then the two triangles are similar.

Similarity Statement:

YXZKJL ~

Examples

• 1) Explain why the triangles are similar and write a similarity statement

• Angle A is congruent• to Angle D• Angle C is congruent• in both triangles • because of vertical angles• So, by AA

B

AC

D

EDECABC ~

Examples

• 2) Are the following triangles similar?

• So, yes by the AA • similarity postulate

Sometimes you mayhave to solve for a piece that isn’t given to us in order to determine if they aresimilar.

x

x + 40 + 88 = 180x = 52

Examples• 3. Explain why the triangles are similar

and write a similarity statement• ΔRQP ~ ΔVUP by the AA postulate

because:

• Suppose RP = 15, RQ = 10 and UV = 7• Find VP and RV• What is the scale factor?

• Write a proportion to • solve:

PP

UQ

x710

15

10

7

1510

7 x

How did I determine this?

Similarity Theorems

If all the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar

1014

18

57

9

18

9

14

7

10

5*Check the side ratios:

612

816 95°

95°

*Check the side ratios and the angle between them

Examples

Examples

Examples

Examples

Examples