HW, packet, red pen, pencil, highlighter, & calculator U8D6 Have Out: HW, packet, red pen, pencil, highlighter, & calculator Jake stands 12 feet away from a tree. He looks into a mirror that he put 2 feet in front of him and can see the top of the tree. His eye level is 5 feet high. How tall is the tree? Bellwork: x +2 5 ft ? 2 ft 10 ft 12 ft

The tree is 25 feet tall. ACD ~  BCE (AA~ Thm) Are the triangles similar? E AD and BE are  to AB A  B (Def of / Right s ) +1 +1 ACD  BCE ( of Incidence =  of Reflection) ACD ~  BCE (AA~ Thm) +1 +1 x D 5 ft 2 ft 10 ft A C B +1 or or… The tree is 25 feet tall. +1

Work on S-56... you have 7 min. to complete it!

12u 9u2 16u 16u2 20u 25u2 S 56 fig. a fig. b fig. c figure c figure a figure b figure d figure e side length perimeter area 1u 2(1)=2u 3(1)=3u 4(1)=4u 5(1)=5u 4u 8u 1u2 4u2 fig. d fig. e 12u 9u2 16u 16u2 20u 25u2 figure c to figure a figure d to figure a figure d to figure b Ratio of: Similarity Side lengths perimeters areas

The area ratio is the square of the ratio of similarity. c) Use the results from part (b) to write a summary of your observations about the relationships between side ratios, perimeter ratios, & area ratios in relation to the ratio of similarity. Look for a pattern & formulate your ideas into a conjecture. The side ratio & perimeter ratios are equal to the ratio of similarity (r). The area ratio is the square of the ratio of similarity.

( ) ( ) For EACH set of similar figures, do all 3 tasks. a) b) Calculate the area of each figure. Write the ratio of the areas, small:large, and reduce. Write the ratio of the shortest pair of corresponding sides, small:large, reduce if possible, and then square it. a) b) 4 5 10 3 6 8 12 24 A= ½ bh A= ½ bh A= ½ (5)(12) A= ½ (10)(24) A= ½ (3)(6) A= ½ (8)(4) = 30 u2 = 120 u2 = 9 u2 = 16 u2 ( ) 2 ( ) 2

( ) For EACH set of similar figures, do all 3 tasks. c) Calculate the area of each figure. Write the ratio of the areas small:large and reduce. Write the ratio of the shortest pair of corresponding sides, small:large, reduce if possible, and then square it. c) 9 4.5 10 20 A= bh A= (9)(20) A= (4.5)(10) = 180 u2 = 45 u2 ( ) 2

6 4 10 12 15 25 30 d) A= + A= + 20 4 8 10 10 4 25 10 = (4•10)+ (½•4•8) = (25•10)+ (½•10•20) = 40 + 16 = 250 + 100 = 56 u2 = 350 u2 ( ) 2 e) The side ratio is the SAME as the ratio of similarity (r) & the area ratio is always the square of r!

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