Geometry IB - HR Date: 3/12/2013 ID CheckObjective: SWBAT identify similar triangles using the AA Similarity Postulate and the SSS and SAS Similarity Theorems.Bell Ringer: See overheadHW Requests: pg 470 #2-26 evensReading to Learn Math WS

HW: Pg 471 #27-30, IB/ Honors 35-37, pg 479 #9-15 odds Announcements:Work Keys Assessment, WednesdayMissing Chapter 5 Test4th S. Crum, C. Harris6th T. Colon, V. Harris, N. Porter, J. Reynolds, Z. Shelton7th K. Bruce, W. Burch, D. Christian, O. Goodrum, J. McLin, M. Robinson, D. Thompson, N. Wooden

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Geometry IB only Date: 2/24/2014 ID CheckObj: SWBAT apply proportions to identify similar polygons and solve problems using the properties of similar polygons.Bell Ringer: pg 470 #12, 14, 16, 18, 20HW Requests: pg 470 #9-21 oddsMake sure to show 1st period the ratios and connection to similarity statements. Add perimeters today.

HW: Pg 470 #23-47 odds, 48 Read Sect. 7.2Announcements:“There is something in every one of you that waits and listens for the sound of the genuine in yourself. It is the only true guide you will ever have. And if you cannot hear it, you will all of your life spend your days on the ends of strings that somebody else pulls.” ― Howard Thurman

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Ex. 2: Comparing Similar Polygons

• Decide whether the figures are similar. If they are similar, write a similarity statement.

15

12

9

6X

W

Z

Y

10

8

6

4Q

P

S

R

15

12

9

6X

W

Z

Y

10

8

6

4Q

P

S

RSOLUTION:

As shown, the corresponding angles of WXYZ and PQRS are congruent. Also, the corresponding side lengths are proportional.

WX

PQ=

15

10=

3

2

XY

QR=

6

4=

3

2

YZ

RS=

9

6=

3

2

WX

PQ=

15

10=

3

2So, the two figures are similar and you can write WXYZ ~ PQRS.

/ A / E; / B / F; / C / G; / D / HAB/EF = BC/FG= CD/GH = AD/EH

The scale factor of polygon ABCD to polygon EFGH is 10/20 or 1/2

Scale factor: The ratio of the lengths of two corresponding sides of similar polygons

Using Similar Polygons in Real Life

In figure, there are two similar triangles . LMN and PQR.

This ratio is called the scale factor.Perimeter of LMN = 8 + 7 + 10 = 25Perimeter of PQR = 6 + 5.25 + 7.5 = 18.75

33.15.7

10

25.5

7

6

8

Using Similar Polygons in Real Life

Ex. 3: Comparing Photographic Enlargements

• POSTER DESIGN. You have been asked to create a poster to advertise a field trip to see the Liberty Bell. You have a 3.5 inch by 5 inch photo that you want to enlarge. You want the enlargement to be 16 inches wide. How long will it be?

Solution:

• To find the length of the enlargement, you can compare the enlargement to the original measurements of the photo.

16 in.

3.5 in.=

x in.

5 in.

x = 16

3.5x∙ 5

x ≈ 22.9 inches

The length of the enlargement will be about 23 inches.

5

3.5

Trip to Liberty Bell

March 24th, Sign up today!

Ex. 4: Using similar polygons

• The rectangular patio around a pool is similar to the pool as shown. Calculate the scale factor of the patio to the pool, and find the ratio of their perimeters.

16 ft 24 ft32 ft

48 ft

• Because the rectangles are similar, the scale factor of the patio to the pool is 48 ft: 32 ft. , which is 3:2 in simplified form.

• The perimeter of the patio is 2(24) + 2(48) = 144 feet and the perimeter of the pool is 2(16) + 2(32) = 96 feet The ratio of the perimeters is

16 ft 24 ft32 ft

48 ft144

96

3

2, or

NOTE:

• Notice in Example 4 that the ratio of perimeters is the same as the scale factor of the rectangles. This observation is generalized in the following theorem.

• Theorem 8.1: If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding parts.

• If KLMN ~ PQRS, then

P

S

Q

RK

N

L

M

KL + LM + MN + NK

PQ + QR + RS + SP=

KLPQ

LMQR

MNRS

NKSP

= = =

Ex. 5: Using Similar Polygons

• Quadrilateral JKLM is similar to PQRS. Find the value of z.

Set up a proportion that contains PQ

15

10J

M L

K

Z

6

S

PQ

R

KLQR

JKPQ

=

156

10Z

=

Z = 4

Write the proportion.

Substitute

Cross multiply and divide by 15.

Ex. 3: Comparing Photographic Enlargements

• POSTER DESIGN. You have been asked to create a poster to advertise a field trip to see the Liberty Bell. You have a 3.5 inch by 5 inch photo that you want to enlarge. You want the enlargement to be 16 inches wide. How long will it be?

• If two polygons are similar, then the ratio of the lengths of two corresponding sides is called the scale factor.

Ex: Scale factor of this triangle is 1:2

3 6

94.5

Identifying Similar Polygons

Similar PolygonsPolygons are said to be similar if :a) there exists a one to one correspondence between their sides and angles.b) the corresponding angles are congruent andc) their corresponding sides are proportional in lengths.

Using Similar Polygons in Real Life

R

SP

Q

A

B C

D

Example 2

Trapezoid ABCD is similar to trapezoid PQRS. List all the pairs of congruent angles, and write the ratios of the corresponding sides in a statement of proportionality.

A P, B Q, C R, D S

PS

AD

RS

CD

QR

BC

PQ

AB

Similar polygons

• If ABCD ~ EFGH,

then

A

B

CD

E

F

G H

HE

DA

GH

CD

FG

BC

EF

AB

Similar polygons

• Given ABCD ~ EFGH, solve for x.

A

B

CD

E

F

G H

2

4

6 x

2x = 24 x = 12

x

6

4

2

• Quadrilateral JKLM is similar to PQRS. Find the value of z.

J

K L

M P

Q

R

S

10

15z

6

z

10

6

15

15z = 60 z = 4

Similar polygons

Given ABCD ~ EFGH, solve for the variables.

A

B

CD

E

F

G H

2

6

5 x

10 y

Geometry IB - HR Date: 3/6/2013 ID CheckObjective: SWBAT demonstrate mastery of Chapter 5 material.

Bell Ringer: Fill out ScantronSubject: Ch. 5 Test Part 1: Scantron Do not write on this copyPart 2: Free Response: You may writeon this copy. This is your copy!

HW: Pg 460 #11-39 odds Due Thurs. Read Sect. 7.2Announcements:

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Geometry IB - HR Date: 2/18/2014 ID CheckObjective: SWBAT write ratios and solve proportions,

Bell Ringer:HW Requests: Chapter Practice Quiz pg 377#1-10 pg 381 #1-4, 6-25 minus 23Stamp HW Period 2 and go over tomorrowHW: Pg 460 #11-39 odds. Read Sect. 7.2Announcements:Chapter 5 Test Thurs.“There is something in every one of you that waits and listens for the sound of the genuine in yourself. It is the only true guide you will ever have. And if you cannot hear it, you will all of your life spend your days on the ends of strings that somebody else pulls.” ― Howard Thurman

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Geometry IB only Date: 2/19/2014 ID CheckObjective: SWBAT write ratios and solve proportions,

Bell Ringer:HW Requests: Chapter Practice Quiz pg 377#1-10 pg 381 #1-4, 6-25 minus 23

HW: Pg 460 #11-39 odds. Read Sect. 7.2Announcements:Chapter 5 Test Thurs.“There is something in every one of you that waits and listens for the sound of the genuine in yourself. It is the only true guide you will ever have. And if you cannot hear it, you will all of your life spend your days on the ends of strings that somebody else pulls.” ― Howard Thurman

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Ratio• Ratio - comparison of two quantities using division.• Ratio of a to b is written as a or a:b.• b • A ratio is a fraction. • Numerator (comparing value); • Denominator (Value we are comparing to).• Keep up with units

Ratio• Ratio - comparison of two quantities using division.

• A classroom has 16 boys and 12 girls.

• Also written as 16 boys, 16:12 or 16 to12 12 girls

• Generally, ratios are in lowest terms:• Ratio of boys to girls is:

16 = 16/4 = 4boys 12 12/4 3 girls

Ratio, continued

• Ratios can compare two unlike things:– Joe earned $40 in five hours – The ratio is 40 dollars or 8 dollars

5 hours 1 hour

– When the denominator is one, this is called a unit rate.

Ratio, continued

Let’s look at a classroom:• Ratios can be part-to-part

– 16 boys15 girls

• Ratios can be part-to-whole– 16 boys

31 students

Ratio, continued

• If a ratio is part-to-whole, you can divide and find a decimal or a percent.

– 16 boys31 students

16.00/31.00 = .516, or 51.6% are boys

Ex. 1. The total # of students in sports is 520. The total # of students in the school is 1850. Find the athlete-to-student ratio to the nearest tenth.

Question: We are comparing what to what? The denominator is the “to what” we are comparing. Remember your units. Ans. 520 athletes =.3 athletes/students 1850 students

Extended ratios a:b:c

Extended Ratios – compare three or more terms. a:b; b:c; a:c

Ex. 3 (Test) The ratio of 3 sides of a ∆ is 4:6:9 and its perimeter is 190 inches. Find the length of the longest side.

Multiplying the ratios by x does not change the value of the ratio. 4x:6x:9xExample (notes) 4x+6x+9x= 190 Side = 90

Exit Ticket: 284, 285 #3, 4, 5, 9, 10, 15, 19

•Proportion – set two ratios = to each other. a = c b,d ≠ 0 b d•Solve similar to equivalent fractions Ex. 3 2 = x 5 15•Solve proportions using Cross products (a*d = b*c) Ex. 3 cont. 2*15 = 5x

•Product of means = product of extremes.•Proportions must have same unit of measure.

Proportion

• Proportion is a statement that says two ratios are equal.– In an election, Damon got three votes for each two votes

that Shannon got. Damon got 72 votes. How many votes did Shannon get?

– Damon 3 = 72 so 3 x 24 = 72 Shannon 2 n 2 x 24 48

n = 48, so Shannon got 48 votes.

Ex. 4 Solve the proportion.

a. ⅔y – 4 = 6 b. 5= x-4 6 12

Proportions - write ratios comparing the measures of all parts of one object with measures of comparable parts of another object. Careful of your units

Ex. 5 A car has length 120 ft and width 64 ft. A toy car is made in proportion to the real car and has a length 9 ft. What is the width of the toy car?1.What are we looking for?2.What are the comparable parts? Or what are we comparing?3.Ratios - what are we comparing?4.Set up the proportion ( two ratios = to each other)5.Check your units. Should have same unit of measure.

Proportion, continued

• Tires cost two for $75. How much will four tires cost?

– # of tires 2 = 4 so 2 x 2 = 4 tires cost 75 n 75 x 2 $150

n = 150, so four tires cost $150

Proportion, continued

• One more way to solve proportions:• Cross multiply.

• 2 = 6 2 x n = 6 x 8 2n = 488 n 2 2

n = 24

Proportion, continued

• Now you try!• Three cans of soup costs $5. How much will 12

cans cost?

• # of cans 3 = 12 3 x 4 = 12 cans cost 5 n 5 x 4 20 dollars

n = 20, so 12 cans cost $20

Geometry IB - HR Date: 3/4/2013 ID CheckObjective: Students will be able to apply properties of bisectors, medians and altitudes in solving for angles and segments of triangles. SWBAT apply properties of inequalities to the measure of the angles of a triangle.Bell Ringer: Go over pg372 #16 make corrections per. 2, 4, 6Homework Requests: Chapter Practice Quiz pg 381, Skip 5, 10-13, 17-19 pg 377 1-10, p 380 #26-33In class: Review SheetParking Lot pg 346 #47HW: Complete Review Sheet, Read Sect. 7.1Announcements:Chapter 5 Test Wed.

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