Geometry IB - HR Date: 3/12/2013 ID Check Objective: SWBAT identify similar triangles using the AA Similarity Postulate and the SSS and SAS Similarity Theorems. Bell Ringer: See overhead HW Requests: pg 470 #2-26 evens Reading to Learn Math WS HW: Pg 471 #27-30, IB/ Honors 35-37, pg 479 #9-15 odds Announcements: Work Keys Assessment, Wednesday Missing Chapter 5 Test 4 th S. Crum, C. Harris 6 th T. Colon, V. Harris, N. Porter, J. Reynolds, Z. Shelton 7 th K. Bruce, W. Burch, D. Christian, O. Goodrum, J. McLin, M. Robinson, D. Thompson, N. Wooden Maximize Academic Potential Turn UP! MAP

Geometry IB only Date: 2/24/2014 ID Check Obj: SWBAT apply proportions to identify similar polygons and solve problems using the properties of similar polygons. Bell Ringer: pg 470 #12, 14, 16, 18, 20 HW Requests: p g 470 #9-21 odds Make sure to show 1 st period the ratios and connection to similarity statements. Add perimeters today. HW: Pg 470 #23-47 odds, 48 Read Sect. 7.2 Announcements: “ 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 ThurmanHoward Thurman Maximize Academic Potential Turn UP! MAP

Ex. 2: Comparing Similar Polygons Decide whether the figures are similar. If they are similar, write a similarity statement.

SOLUTION: As shown, the corresponding angles of WXYZ and PQRS are congruent. Also, the corresponding side lengths are proportional. WX PQ = = 3 2 XY QR = 6 4 = 3 2 YZ RS = 9 6 = 3 2 WX PQ = = 3 2  So, the two figures are similar and you can write WXYZ ~ PQRS.

/ A  / E; / B  / F ; / C  / G ; / D  / H AB/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 = = 25 Perimeter of  PQR = = 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= x∙ 5 x ≈ 22.9 inches  The length of the enlargement will be about 23 inches Trip to Liberty Bell March 24 th, 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 ft24 ft 32 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 ft24 ft 32 ft 48 ft , 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 KL + LM + MN + NK PQ + QR + RS + SP = KL PQ LM QR MN RS NK SP = = =

Ex. 5: Using Similar Polygons Quadrilateral JKLM is similar to PQRS. Find the value of z. Set up a proportion that contains PQ KL QR JK PQ = Z = 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:

Identifying Similar Polygons Similar Polygons Polygons 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 and c) their corresponding sides are proportional in lengths.

Using Similar Polygons in Real Life 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

Similar polygons If ABCD ~ EFGH, then A B C D E F G H

Similar polygons Given ABCD ~ EFGH, solve for x. A B C D E F GH x 2x = 24 x = 12

Quadrilateral JKLM is similar to PQRS. Find the value of z. J KL M P Q R S z 6 15z = 60 z = 4

Similar polygons Given ABCD ~ EFGH, solve for the variables. A B C D E F GH x 10 y

Geometry IB - HR Date: 3/6/2013 ID Check Objective: SWBAT demonstrate mastery of Chapter 5 material. Bell Ringer: Fill out Scantron Subject: Ch. 5 Test Part 1: Scantron Do not write on this copy Part 2: Free Response: You may write on this copy. This is your copy! HW: Pg 460 #11-39 odds Due Thurs. Read Sect. 7.2 Announcements: Maximize Academic Potential Turn UP! MAP

Geometry IB - HR Date: 2/18/2014 ID Check Objective: 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 Stamp HW Period 2 and go over tomorrow HW: Pg 460 #11-39 odds. Read Sect. 7.2 Announcements: 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 ThurmanHoward Thurman Maximize Academic Potential Turn UP! MAP

Geometry IB only Date: 2/19/2014 ID Check Objective: 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. 7.2 Announcements: 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 ThurmanHoward Thurman Maximize Academic Potential Turn UP! MAP

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 as16 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 boys 15 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 boys 31 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 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:9x Example (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 n = 48, so Shannon got 48 votes.

Ex. 4 Solve the proportion. a. ⅔y – 4 = 6 b. 5= x

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 = 48 8 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 Check Objective: 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, 6 Homework Requests: Chapter Practice Quiz pg 381, Skip 5, 10-13, pg , p 380 #26-33 In class: Review Sheet Parking Lot pg 346 #47 HW: Complete Review Sheet, Read Sect. 7.1 Announcements: Chapter 5 Test Wed. Maximiz e Academi c Potential Turn UP! MAP