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Congruent and similar_shapes

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  • 1. Congruent and similarCongruent and similarshapesshapesCongruentshapesSimilarshapes
  • 2. Congruent shapesCongruent shapes
  • 3. 1. Which of these shapes are1. Which of these shapes arecongruentcongruent to theto the yellowyellow one?one?25431768AnswersHintsStart page
  • 4. CongruentCongruent shapes are all shown inshapes are all shown inyellowyellow – were you right?– were you right?5431768Start page2
  • 5. What makes a pair of shapesWhat makes a pair of shapes““congruentcongruent”?”?Same anglesSame anglesSame side lengthsSame side lengthsCan be rotated or a mirror imageCan be rotated or a mirror imageA cut-out of one shape will always fitA cut-out of one shape will always fitexactly over the otherexactly over the otherClick the green box if you want to go back toClick the green box if you want to go back tothe first “congruent shapes” question page.the first “congruent shapes” question page.Question pageStart page
  • 6. 2. Which of these shapes are2. Which of these shapes arecongruentcongruent to theto the yellowyellow one?one?AnswersStart page251346789
  • 7. CongruentCongruent shapes are all shown inshapes are all shown inyellowyellow – were you right?– were you right?Start page251346789
  • 8. Similar shapesSimilar shapes
  • 9. Which of these shapes areWhich of these shapes are similarsimilarto theto the yellowyellow one?one?25431768AnswersHintsStart page
  • 10. SimilarSimilar shapes are all shown inshapes are all shown inyellowyellow – were you right?– were you right?25431768Start page
  • 11. What makes a pair of shapesWhat makes a pair of shapes““similarsimilar”?”?Same anglesSame anglesSides in the same proportionSides in the same proportionCan be rotated or reflectedCan be rotated or reflectedOne is an enlargement of the otherOne is an enlargement of the otherScale factor gives degree of enlargement:Scale factor gives degree of enlargement:– Scale factor 2Scale factor 2 →→ size is doubledsize is doubled– Scale factor 0.5Scale factor 0.5 →→ size is halvedsize is halved– Scale factor 1Scale factor 1 →→ size doesn’t changesize doesn’t change →→ congruent toocongruent tooClick the green box if you want to go back to theClick the green box if you want to go back to the“similar shapes” question page.“similar shapes” question page.Question pageStart page
  • 12. Using similarityUsing similarity9cm 12cm6cmaSince shapes are similar, theirsides are in the same proportionMultiply both sides by 12=> 12 x 6 = a9=> a = 12 x 2 = 4 x 23 1Start page=> 6 = a9 12=> a = 8cm
  • 13. Which of these shapes areWhich of these shapes are similarsimilarto theto the yellowyellow one?one?(They aren’t drawn to scale)(They aren’t drawn to scale)432156AnswersStart page6969464.53121891248
  • 14. SimilarSimilar shapes are shown inshapes are shown in yellowyellow– were you right?– were you right?Start page9656964.53312181912464248
  • 15. Scale factor =Scale factor = new valuenew valueold valueold value..8cm 12cmScale factor?Scale factor?5cm7.5cmNew value =Old valueNew value =Old valueStart page12 = 3 or 1.58 2Can you see the relationship between the two scale factors?8 = 212 3
  • 16. Using scale factorUsing scale factor9cm aEnlarge withscale factor 3b15cma = 9 x 3 = 27cmSF = new/old = 9/27 = ⅓What will thescale factor be?b = 15 x ⅓ = 15 ÷ 3 = 5cmStart pageOR reciprocal of 3 = ⅓
  • 17. Similar shapes - summarySimilar shapes - summaryabcxyzRatio a:b:c = ratio x:y:zSo: a = x a = x b = yb y c z c zTo see whether 2 shapes are similar, put eachratio in its simplest form and see if they match.Scale factor = new measurementold measurement- Scale factor more than 1 => shape gets bigger- Scale factor less than 1 => shape gets smaller- Congruent shapes are similar shapes with SF = 1Old measurement x SF = new measurementRemember: only side lengths change; angles stay the same!SFnewold