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Identify the means and the extremes in the proportion. w x = y z Means: y & x Extremes: w & z Identify the means and the extremes in the proportion. 9 6+y = 12w 5 Means: 6 + y & 12w Extremes: 9 & 5 Identify the means and the extremes in the proportion. q+3 5m = 2 q Means: 5m & 2 Extremes: q + 3 & q Identify the means and the extremes in the proportion. m a = T h Means: a & T Extremes: m & h Factor completely. x2 – 225 (x + 15)(x – 15) Factor completely. 5x2 – 125y4 5(x2 – 25y4) 5(x + 5y2)(x – 5y2) Factor completely. 12x13 – 75x 3x(4x12 – 25) 3x(2x6 + 5)(2x6 – 5) Factor completely. x2 + 12x + 32 (x + 4)(x + 8) Factor completely. x2 – 12x + 32 (x – 4)(x – 8) Factor completely. x2 – 4x + 32 (x + 4)(x – 8) Factor completely. x2 + 14x + 45 (x + 9)(x + 5) Factor completely. x2 + 15x + 36 (x + 12)(x + 3) Factor completely. 8x2 + 2x – 21 8x2 + 14x – 12x – 21 2x(4x + 7) – 3(4x + 7) (4x + 7)(2x – 3) 8 •-21 = -168 14 & -12 Factor completely. 12x2 + 53x + 20 12x2 + 48x + 5x + 20 12x(x + 4) + 5(x + 4) (x + 4)(12x + 5) 12 •20 = 240 48 & 5 Factor completely. 12 •-11 = -132 -22 & 6 12x2 – 16x – 11 12x2 – 22x + 6x – 11 2x(6x – 11) + 1(6x – 11) (2x + 1)(6x – 11) Factor completely. 32x2 – 36x + 9 32x2 – 24x – 12x + 9 8x(4x – 3) – 3(4x – 3) (8x – 3)(4x – 3) 32 • 9 = 288 -24 & -12 Factor completely. x2 – 15x + 36 (x – 12)(x – 3) Factor completely. x2 + 4x – 45 (x – 9)(x + 5) Factor completely. 2x2 – 28x + 90 2(x2 – 14x + 45) 2(x – 9)(x – 5) Factor completely. 3x2 – 27x – 108 3(x2 – 9x – 36) 3(x – 12)(x + 3) Find the missing side of the triangle. x 16 12 122 + 162 = x2 144 + 256 = x2 400 = x2 20 = x Find the missing side of the triangle. x 3 2 22 + 32 = x2 4 + 9= x2 13 = x2 3.6 ≈ x Find the missing side of the triangle. x 10 18 102 + 182 = x2 100 + 324= x2 424 = x2 20.6 ≈ x Find the missing side of the triangle. 19 12 x 122 + x2 = 192 144 + x2 = 361 x2 = 217 14.7 ≈ x Find the missing side of the triangle. 70 x 30 302 + x2 = 702 900 + x2 = 4900 x2 = 4000 63.2 ≈ x Find the missing side of the triangle. 25 x 7 72 + x2 = 252 49 + x2 = 625 x2 = 576 24 = x Do the following lengths form a right triangle? 7, 24, 25 72 + 242 ? 252 49 + 576 ? 625 625 = 625 yes! Do the following lengths form a right triangle? 5, 13, 12 52 + 122 ? 132 25 + 144 ? 169 169 = 169 yes! Do the following lengths form a right triangle? 9, 12, 15 92 + 122 ? 152 81 + 144 ? 225 225 = 225 yes! Do the following lengths form a right triangle? 12, 20, 18 122 + 182 ? 202 144 + 324 ? 400 468 ≠ 400 no! Do the following lengths form a right triangle? 19, 17, 18 172 + 182 ? 192 289 + 324 ? 361 613 ≠ 361 no! Do the following lengths form a right triangle? 2, 7, 8 22 + 72 ? 82 4 + 49 ? 64 53 ≠ 64 no! DBA ~ ∆ _______ DAC ∆ABC ~ ∆______ B A D C YBS ~ ∆ _______ BUS ∆YUB ~ ∆______ U B S Y PMQ ~ ∆ _______ QMR ∆PQR ~ ∆______ P Q M R GIH ~ ∆ _______ HIJ ∆GHJ ~ ∆______ G H I J ∆ABC ~ ∆DEF. Find the value of x. F C B 4x 4x = 3x + 3 A 30 27 D 30 E 90x + 90 = 108x 90 = 18x x=5 ∆GHI ~ ∆JKL. Find the value of x. H J L 2x + 5 2x + 5 = 3x – 20 K G 10 I 9 16x + 40 = 27x – 180 220 = 11x 8 x = 20 ∆MNO ~ ∆PQR. Find the value of x. P M N Q O 6x + 1 = 46.5 5x – 6 28.5 34.5 R 232.5x – 279 = 171x + 28.5 61.5x = 307.5 x=5