6-5 Similar Polygons notes
6-5 Similar Polygons notes
6-5 Similar Polygons notes
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Integrated I6-5 <strong>Similar</strong> <strong>Polygons</strong>6-5 <strong>Similar</strong> <strong>Polygons</strong>Warm-up1. Name the sides of the polygon FGHIJGFHJSolve each proportion2.3 x=8 24x = 93.4 20=5 aa = 254.2n2=20 10n = 2IFG, GH, HI, IJ,JF6-5 <strong>Similar</strong> <strong>Polygons</strong><strong>Similar</strong> Figures – two figures with the same shape. They may be the same size or differentsizes.Ex:Side-note: ~ means similar toScale drawings – a drawing that represents an actual object. Objects in a scale drawing havethe same shape as in real life.Ex: A road map is a scale drawing of roads in an area.Scale – the ratio of the size of the drawing to the actual size of the object it represents.Ex: The scale as “1 in. = 50 mi.”, can be found on a road map. It tells you howdistances on the map correspond to distances on the actual road.<strong>Similar</strong> polygons have corresponding angles congruent and corresponding sides inproportion.Side-note: Two triangles are similar if they have two pairs of correspondingangles congruent.6-5 <strong>Similar</strong> <strong>Polygons</strong>
Integrated I6-5 <strong>Similar</strong> <strong>Polygons</strong>Properties of similar triangles• Must have at least 2 pairs of corresponding angles that are congruent (thesame)…more specifically, corresponding angles are congruent.• Corresponding sides are in proportion. Their lengths have the same ratio.Example 1Trapezoid LMNP ~ trapezoid QRSTUse the figures to find each measure.1. LP 2. QR 3. ∠ MSolution1. Use a proportion involving LP and QT, the lengths of the side corresponding toLP . Look at the trapezoids for corresponding sides whose lengths are know suchas NP and ST.LP NP= ← Set up ratios to correspond. Here the lengths from the largerQT ST trapezoid are on the top and those of the smaller trapezoid areLet x = LPx 8 =2 66x = 16x = 2 2/3So, LP = 2 2/3 or 2.67 units6-5 <strong>Similar</strong> <strong>Polygons</strong>
Integrated I6-5 <strong>Similar</strong> <strong>Polygons</strong>2. Use a proportion. Let y = QR. LM corresponds to QR .QR STlittle =LM NPbigy 6 =4 88y = 24y = 3So, QR = 33. ∠ M corresponds to ∠ R …
Integrated I6-5 <strong>Similar</strong> <strong>Polygons</strong>*Vertical angles are equal.Since we have two pairs of corresponding angles that are congruent (equal), thetriangles are similar.b. big littleBC AB=CE DElet x = AB500 = x9 56500(56) = 9xx = 3, 111.1 feetThe distance across the lake from point A to point B is about 3111 ft.Example 4What is the actual length of the international basketball court if the drawing is 5cm in length?Example 3Scale: 1 cm = 5.2 mSolutionscale drawing measurementactual measurement1 5=5.2 a1a= 26a = 26The basketball court is 26 m long.Let a = the actual measurement of the court6-5 <strong>Similar</strong> <strong>Polygons</strong>
Integrated I6-5 <strong>Similar</strong> <strong>Polygons</strong>Example 5Use the map below. The scale is 1 in = 200 yd.How far is it (along the streets) from 26 Greenview Road to the library?LibraryJason StreetLibrary WayCourt StreetMain StreetGreenview RoadScale26200 yd.SolutionUse a ruler to measure the distance on the map and use the scale to find the actualdistance.6-5 <strong>Similar</strong> <strong>Polygons</strong>
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