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Similar Triangles

Similar Triangles. Area & Volume Scale Factor OCR Module 9. D J Millward 2008. MENU. Stage 7 Recap. AREA. VOLUME. Similar shapes. FROM STAGE 7. Are Enlargements of each other Corresponding angles are equal Sides are related by the same scale factor. Similar Triangles.

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Similar Triangles

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  1. Similar Triangles Area & Volume Scale Factor OCR Module 9 D J Millward 2008

  2. MENU Stage 7 Recap AREA VOLUME

  3. Similar shapes FROM STAGE 7 • Are Enlargements of each other • Corresponding angles are equal • Sides are related by the same scale factor

  4. Similar Triangles Triangles are similar if matching angles remain the same size. 100º 30º 50º 100º 30º 50º

  5. To calculate a length 5 15 5 4 x 3 x 3 6 Scale factor 3 15 12 1 3 18 Scale factor 1/3

  6. A D E C B Harder example 3 4 6 Triangle ABC is similar to triangle ADE. DE is parallel to BC. Calculate the length of BC

  7. 3 E D 4 Harder example A 9 6 C 12 B 9 3 x 3

  8. …and then… AB & DE are parallel Explain why ABC is similar to CDE <CED = <BAC Alternate Angles 5 A B <EDC = <ABC Alternate Angles <ECD = <ACB Vert Opp Angles 3 C 6 E D ? Triangle ABC is similar to Triangle CDE

  9. …and then… Calculate the length of DE AC corresponds to CE Scale Factor = 2 5 A B AB corresponds to DE DE = 2 x AB 3 C DE = 10cm 6 E D ?

  10. Summary – Similar shapes • To calculate missing sides, we first of all need the scale factor • We then either multiply or divide by the scale factor • To show that 2 shapes are similar we can either show that all of the sides are connected by the scale factor or show that matching angles are the same

  11. AREA SCALE FACTOR 2cm 10cm² 5cm ENLARGE rectangle Scale Factor 2 40cm² 4 cm 10 cm AREA SCALE FACTOR = 4

  12. AREA SCALE FACTOR 2cm 10cm² 5cm ENLARGE rectangle Scale Factor 3 90cm² 6 cm 15 cm AREA SCALE FACTOR = 9

  13. AREA SCALE FACTORS • Reflect the Length Scale Factor 2² 3² AREA SCALE FACTOR = LENGTH SCALE FACTOR SQUARED ASF = LSF²

  14. Example Questions - AREA Calculate the unknown areas Q1 Q2 5 cm 10 cm² 40 cm² 4 cm 12 cm² 8 cm Q3 15 cm 9 cm² 4 cm² 108 cm² 2 cm 3 cm

  15. Example Questions - SIDES Calculate the unknown lengths Q1 Q2 3 cm 10 cm² 250 cm² 2 cm 12 cm² y 10 cm Q3 6 cm x 18 cm² 8 cm² 48 cm² 2 cm 3 cm z

  16. VOLUME SCALE FACTOR 1 cm 3 cm 6 cm³ 162 cm³ 2 cm 3 cm ENLARGE cuboid Scale Factor 3 6 cm 9 cm = 3³ VOLUME SCALE FACTOR = 27

  17. VOLUME SCALE FACTOR 4 cm 8 cm³ 8 cm 64cm³ ENLARGE cylinder Scale Factor 2 Volume Scale Factor = 2³ VOLUME SCALE FACTOR = LENGTH SCALE FACTOR CUBED VSF = LSF³

  18. Example Questions - VOLUME Q2 Q1 2 cm 5 cm³ 8 cm³ 3 cm 27 cm³ 4.5 cm 135 cm³ 6 cm Q3 40 cm³ 5 cm³ 4 cm 2 cm

  19. Example Questions - SIDES Q2 Q1 2 cm 5 cm³ 6 cm³ 1.5 cm 384 cm³ a 4 cm 6 cm b 40 cm³ Q3 120 cm³ 15 cm³ 3.6 cm 1.8 cm c

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