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12 16 A B C DE F G H I J KL M N a b c d 45º e f g h 60º i j k m Chapter 8 TestUse your calculator. Show your work! Given: AEFJ is a Rectangle. DEFG is a rectangle. DEFG is congruent to CDGH. ACNK is a Square. KNHJ is a Rectangle. NH = 1/3 NC. AB = 1/3 BC. Your first instructions were to label and highlight all of the given information… g=1/3 f or f = 3g k = 1/3 BC or BC = 3k Notice that all triangles involved in solving a – m are right triangles… Your next suggestion was to oslve from right to left… For a and c, we are given two sides… Tan a = opp. / adj. Tan a = 16 / 12 a = tan-1 (16/12) a = 53.13 ~ 53 degrees Tan c = opp. / adj. Tan c = 12 / 16 c = tan-1 (12/16) c= 36.87 ~ 37 degrees 53 37 For b and d, these may be found either by: Supplmentary angles A + b = 90 b + c = 90 OR alt. int. angles a = d and b = c 53 37 Because we have two Congruent rectangles, their diagonals are congruent. We can solve for e with sin or cos from either angle… but why not just use the Pythagorean theorem. A^2 + B^2 = C^2 12^2 + 16^2 = C^2 144 + 256 = C^2 400 = C^2 C = 20 20 To solve for f and g, we use our properties of rectangles. The opposite side is 16, so CH is also 16. f = 3g. 3g + g = 16. G = 4 F = 3g = 3(4) = 12 12 4

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16 A B C DE F G H I J KL M N a b c d 45º e f g h 60º i j k m Chapter 8 TestUse your calculator. Show your work! Given: AEFJ is a Rectangle. DEFG is a rectangle. DEFG is congruent to CDGH. ACNK is a Square. KNHJ is a Rectangle. NH = 1/3 NC. AB = 1/3 BC. 12 4 A triangle… whose angles add up to 180 degrees… If N is 90 (square) and we see 60… a ___-60-90 triangle…. 13.86 5.66 12 Because ACNK is a square. 3 Because k = 1/3 BC … 4k = 12 12 And finally, m may be solved with the opposite and adjacent sides. Tan m = 3 / 12 m = tan-1 (3/12) m = 14.04 ~ 14 degrees.

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12 16 A B C DE F G H I J KL M N a b c d 45º e f g h 60º i j k m Chapter 8 TestUse your calculator. Show your work! Given: AEFJ is a Rectangle. DEFG is a rectangle. DEFG is congruent to CDGH. ACNK is a Square. KNHJ is a Rectangle. NH = 1/3 NC. AB = 1/3 BC. This was supposed to be an easy test. You were given every opportunity to get help... This test allowed you to USE YOUR CALCULATOR AND YOUR NOTES! AND IT WAS TAKE HOME! It would not be fair to the students to did take advantage of this opportunity, and tutoring, to redo this test. So NO DO-OVERS! So NO CORRECTIONS! So instead of this trig-only test, if you wish to improve your grade, an alternate test on Chapter 8 (section 8-1 – 8-5) will be given. MUST BE COMPLETED ON YOUR OWN TIME. TEST WILL BE DUE BY FRIDAY, APRIL 4 TH. NO EXCEPTIONS!

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6.4 Rhombuses, Rectangles, and Squares

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