Similar Triangles

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Similar Triangles

  1. 1. Similar Triangles Lesson 8-3 Focus – Apply the properties of similar triangles and tomorrow, prove that triangles are similar. WA State Standards: G.3.A and G.3.B
  2. 2. Congruent Triangles A 100° 115 f t ft 0 10 45° 35° B 150 ft C …have matching angles that are congruent. …have matching sides that are congruent. F 150 ft 45° E 35° t 0f 10 115 ft 100° D
  3. 3. Congruent Triangles A m∠C = m∠E 100° 115 f t m∠A = m∠D ft 0 10 45° 35° m∠B = m∠F B 150 ft C …have matching angles that are congruent. …have matching sides that are congruent. F AC ≈ DE 150 ft 45° E 35° t 0f CB ≈ EF 10 115 BA ≈ FD ft 100° D
  4. 4. Similar Triangles  IF and ONLY IF − Vertices match up so corresponding angles are congruent. − Corresponding sides are in proportion. 4 Ratios of each side are 3 12 30° 12 30° 16 16 75° 75° 6 75° 75° 8
  5. 5. Triangle Similarity Postulate  If two angles of one triangle are equal in measure to two angles of another triangle, then the two triangles are similar. AA (angle/angle) similarity
  6. 6. AA? • You will also see: • SAS • Side/Angle/Side • ASA • Angle/Side/Angle • SSS • Side/Side/Side Knowing these letters will help with proofs later.
  7. 7. Are they similar? Only one angle is given as congruent. Two must be given to use Angle/Angle or AA Similarity.
  8. 8. Are they similar? Use Angle/Angle or AA Similarity. Two congruent angles show triangles are similar.
  9. 9. Similar? 30° Find the missing side of each 30° triangle to find two 30° angles and a 120° angle 120° for each of these similar triangles. 30°
  10. 10. Is VABC similar to VAEF? A E F Sometimes it helps to separate the two triangles and look at each angle separately. B C
  11. 11. Find the missing side 30° We previously 21 ft determined that these triangles are similar. 7 ft 30° We can set up ratios to find the missing 28 ft side. n ft 120° Start with a label on top and bottom. 30° short 21 7 = = long 28 n
  12. 12. In today’s lesson… • We found that congruent triangles have both congruent angles and sides. • Similar triangles have congruent angles. • We can use the AA similarity to determine if triangles are similar. • We can use ratios to determine a missing side’s length when similar triangles are used. WA State Standards: G.3.A and G.3.B
  13. 13. Assign: 453: 4-8; 12-13 457: 1-4 This statue can be seen in downtown Seattle in the Pacific Place Mall on the main level.
  14. 14. Day Two
  15. 15. Overlapping Triangles  Sometimes useful to redraw as separate triangles. Name the AF ≈ AC congruent sides and A A angles. AE ≈ AB EF ≈ BC E F B C
  16. 16. Is VABC similar to VAEF?
  17. 17. Prove: A line is drawn from a point on one side of a triangle parallel to another side forms a triangle similar to the original triangle.
  18. 18. Given: Prove:
  19. 19. Overlapping Similar Triangles Theorem  If a line is drawn from apoint on one side of a triangle parallel to anoter side,  Then it forms a triangle similar to the original triangle.
  20. 20. Assign: 453: 9; 14, 16, 21a 457: 5-7

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