Monday Homework: Textbook 2. 5 pg Monday Homework: Textbook 2.5 pg.74 #1, 2, 4, 8, 9, 10, 11, 13, 17, 18, (19 bonus) & enter 2.1 book assignment if not done 1st: Fill out planner 2nd: Put 2.1 in Binder (lined paper – even if you didn’t submit it) 3rd: Begin Warm Up, on front, one on back 4th: Comp book & pencil on desk 5th: Practice Math Facts 5 minutes for everything Solve for k Solve for z Use this homework assignment. Equations for warm up that we talked about last week. I am finished with this lesson. Solve for y Math Facts

Challenge of The Week: due next Monday 1st. Research then: 2nd: Make mini-poster or type a couple paragraphs. Include the following: A. Who was Fibonacci? What is known about him and his life? List a few of his contributions. B. What is the Fibonacci Sequence? How is the pattern formed? What is its mathematical connection to nature? Give some examples. C. Include a picture(s) of an example from nature. NO COPY and pasting! It must be in your own words!

Dress Code Math Facts This Week: Monday: Similar Figures Tuesday: Quiz Wednesday: Perimeter & Area of Similar Figures Thursday: Dilations Friday: Begin Review for Unit 2 Exam & District Exam Video: How do animators use math?

2.5 Similar Figures Essential Question: How can you determine if two figures are similar or not? Trapezoids ABCD and EFGH are congruent. Congruent: (same corresponding side lengths & angles) Review on Congruent Figures: 1. Which side of EFGH is corresponds to side AD? 2. The perimeter of ABCD is 30 centimeters. What is the value of x? 3. What is the length of side EF? 4. What is the length of side GF?

SIMILAR FIGURES Two figures are similar if: 1. The measures of their corresponding angles are equal. 2. The ratios of the lengths of the corresponding sides are proportional. (same shape but not necessarily same size) The symbol ~ a “tilde” means “is similar to.” SIMILAR FIGURES

SIMILAR FIGURES Big 𝑇𝑟𝑖𝑎𝑛𝑔𝑙𝑒 𝑆𝑚𝑎𝑙𝑙 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 𝑆𝑚𝑎𝑙𝑙 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 𝐵𝑖𝑔 𝑇𝑟𝑖𝑎𝑛𝑔𝑙𝑒 =

Example 1- Are Two Triangles Similar? Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar. E AB corresponds to DE. 16 in 10 in A C 28 in BC corresponds to EF. 4 in D 7 in 40 in F AC corresponds to DF. B AB DE = ? BC EF = ? AC DF Write ratios using the corresponding sides. 4 16 = ? 7 28 = ? 10 40 Substitute the length of the sides. 1 4 = ? 1 4 = ? 1 4 Simplify each ratio. Since the ratios of the corresponding sides are equivalent, the triangles are similar.

Example 2- Find missing side of similar figures

Your Turn: The triangles are similar. Find x

Example 3: Indirect Measurement The inside triangle is similar in shape to the outside triangle. Find the height of the outside triangle. 8 h 14 30 = Write a proportion. 8 h 14 30 Use compatible numbers to estimate. = Simplify. 8 • 30 = 14 • h Cross multiply. 240 = 14h Divide each side by 3 to isolate the variable. 17 ≈ h The outside triangle is about 17 feet tall.

Your Turn: City officials want to know the height of a traffic light. What is the height of the traffic light? h ft 25 ft

White Boards

Draw a line below your notes and answer one of the following question using complete sentences- True or False: If you subtract the same amount from each side of the figure, the resulting ratio will be proportional? How would you demonstrate to another person if two figures are similar? Are two figures that have the same size AND shape similar? Justify your answer with an explanation.

textbook 2.5 pg 74 #1, 2, 4, 8, 9, 10, 11, 13, 17, 18, (19 bonus)

Extra Practice The width of the smaller rectangular box is 6.25 inches. The width of a similar larger rectangular box is 8.75 inches. Estimate the length of the larger rectangular box. A. about 16 in. B. about 17 in. C. about 18 in. D. about 19 in.