Congr similar


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Congr similar

  1. 1. What We Hope You Learn bythe End of this Presentation: What is a polygon? What are the different types ofpolygons? What is a congruent polygon? What is a similar polygon? What are some examples of thesepolygons?
  2. 2. A polygon is a plane having three or moresides.Convex polygon: all the sides are pushedoutward.Concave polygon: at least two sides arepushed inward.Regular polygon: all the sides have the samelength and their angles are all the same size.
  3. 3. Take a minute to match thename up with the figure . . .
  4. 4. Congruent polygons are polygonsthat have the same size and thesame shape.fact:fact:Congruent shapes have all theirsides and angles congruent.
  5. 5. Notice how the secondfigures have the same shapeand size of the first – theymatch exactly.Now we are going to take alook at similar polygons . . .
  6. 6. Can you find the similarmatches?
  7. 7. Can you find similar polygons?(1) Triangle(2) Rectangle(3) Pentagon(4) Hexagon(5) OctagonSame shapeDifferent sizeAngle does not changeEnlargementReduction
  8. 8. Now, let’s define similar !!Definition:Figures that have exactly same shapeare called similar figures.(1) In polygons, the size of angles does not change.(2) One figure is an enlargement or reduction of theother.(3) Congruent figures are similar because they gavethe same shape.Properties:
  9. 9. How can we know the lengthof sides in similar figures?If two figures are similar, one figure is anenlargement of the other. The size-changefactor tells the amount of enlargement orreduction.Example 1: If a copy machine is used to copy a drawing or picture, thecopy will be similar to the original.Original CopyExact CopyCopy machine set to 100%Size-change factor isOriginal CopyEnlargementCopy machine is set to 200%Size-change factor isOriginal CopyReductionCopy machine is set to 50%Size-change factor is1X 2X 12x
  10. 10. Example 2: The triangles CAT and DOG are similar. Thelarger triangle is an enlargement of the smaller triangle. Howlong is side GO?CAT GOD1.5 cm3 cm2 cm3 cm6 cm? cmEach side and its enlargementform a pair of sides calledcorresponding sides.(1) Corresponding side of TC --> GD(2) Corresponding side of CA--> DO(3) Corresponding side of TA--> GOLength ofcorrespondingsidesGD=3TC=1.5DO=6CA=3GO=?TA=2Ratio of Lengths 3/1.5=2 6/3=2 ?/2=2The size-change factor is 2x.
  11. 11. 1.5 cm2 cm3 cmTC(1) Each side in the larger triangle is twice the size ofthe corresponding side in the smaller triangle.AGDO3 cm6 cm? cm(2) Now, let’s find the length of side GOi) What side is corresponding side of GO? TAii) What is the size-change factor? 2Xiii) Therefore, GO= size-change factor x TAiv) So, GO= 2 x 2 = 4 cm
  12. 12. What we just learnedabout similar polygons ?Same shapeDifferent sizeCorresponding side Size-change factorNot change angleSimilar polygons
  13. 13. Example 1: Quadrangles ABCD and EFGH are similar.How long is side AD? How long is side GH?15 cm? cm18 cm12cm7cm6cm4cm?cmBCADHEGF(1) What is size-change factor?(2) What is corresponding sideof AD ?(3) How long is side AD?(4) What is corresponding sideof GH?(5) How long is side GH?12÷ 4= 3 & 18÷ 6=3EHAD = 5CD7 x 3 = GH, GH = 21
  14. 14. Example 2 : Figure MORE is similar to Figure SALT.Select the right answer with the one ofthe given values below.(1) The length of segment TL.a. 6 cm b. 6.5 cm c. 7 cm d. 7.5 cm(2) ER corresponds to this segment.a. TS b. TL c. AL d. SA(3) EM corresponds to this segment.a. TS b. TL c. SA d. AL(4) The length of segment MO.a. 6 cm b. 6.5 cm c. 7 cm d. 7.5 cmQuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
  15. 15. A polygon is a plane having three or more sides.Congruent polygons are polygons that havethe same size and the same shape.Similar polygons are polygons that havethe same shape.congruent congruentsimilar similar