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Download Geometry Notes 7-2 Ratios in Similar Polygons Recall, in congruent
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Geometry Notes 7-2 Ratios in Similar Polygons Recall, in congruent polygons, corresponding sides were congruent and corresponding angles were congruent. We also have a relationship called similar polygons. The following pairs of polygons are similar. In similar polygons, corresponding angles are congruent and corresponding sides are proportional. (In other words, the figures are the same shape but not the same size.) Ex. 1: Determine if the triangles are similar. If so, list the pairs of congruent angles and the corresponding sides. Then write the similarity statement. Are all the pairs of angles congruent? m∠M = m∠T = 90 − 63 = 27°, so yes. € € Are the sides proportional? 1 2 2.2 = = (All = 2) so yes. .5 1 1.1 Congruent Angles ∠M and ∠T ∠N and ∠Q ∠P and ∠R Corresponding Sides MN and TQ NP and QR MP and TR The triangles are similar, and we write this as ΔMNP ~ ΔTQR . € .5 Ex. 2: Determine if the two figures are similar. If so, write the similarity ratio and the similarity statement. a) Rectangles have 4 right angles, so their angles are congruent. 6 9 3 = yes - similarity ratio = 4 6 2 Both are rectangles. Similarity statement: ABCD ~ EFGH € b) Triangle PQR is isosceles, so its base angles are equal. 180 − 36 144 m∠P = m∠R = = = 72° 2 2 Those are NOT the same as the base angles in triangle STW, so the figures are not similar. € Ex. 3: ABCD~EFGH. Solve for x. 4 6 = x 8 6x = 4 (8) = 32 32 x= = 5.3 6 € A D 4 B H E x 6 C F 8 G C x+6 D 3 Ex. 4: ABC~EDF. Solve for x. E A x+2 5 B x+2 3 = x+6 5 5( x + 2) = 3( x + 6) F 5x + 10 = 3x + 18 2x = 8 x=4 € 1 . If the 30 length of the model is 10 inches, what is the length of the actual sailboat in feet? Ex. 5: The ratio of a model sailboat’s dimensions to the actual boat’s dimensions is 1 10 in = 30 x in x = 30(10 in) = 300 in € BUT the question asked for the answer in feet, so we need to convert inches to feet. 300 in ÷12 in/ft = 25 ft €