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Similar Triangles Focus – Apply the properties of similar triangles and tomorrow, prove that triangles are similar. Lesson 8-3 WA State Standards: G.3.A and G.3.B
Congruent Triangles …have  matching angles  that are  congruent.   …have  matching sides  that are  congruent. A B C D F E 100° 35° 45° 115 ft 150 ft 100 ft 150 ft 115 ft 100 ft 35° 100° 45°
Congruent Triangles …have  matching angles  that are  congruent.   …have  matching sides  that are  congruent. A B C D F E 100° 35° 45° 115 ft 150 ft 100 ft 150 ft 115 ft 100 ft 35° 100° 45°
Similar Triangles ,[object Object],[object Object],[object Object],30° 30° 75°  75° 75°  75° 16 12 12 16 6 8 Ratios  of each side are
Triangle Similarity Postulate ,[object Object],[object Object],[object Object]
AA? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Are they similar? ,[object Object]
Are they similar? Use  Angle/Angle  or  AA Similarity .  Two  congruent angles show triangles are similar.
Similar? ,[object Object],120° 30° 30° 30°
Is  ABC similar to  AEF? A E F C B Sometimes it helps to separate the two  triangles and look at each angle separately.
Find the missing side ,[object Object],[object Object],120° 30° 30° 30° 7 ft 21 ft 28 ft n  ft
In today’s lesson… ,[object Object],[object Object],[object Object],[object Object],WA State Standards: G.3.A and G.3.B
Assign: 453: 4-8;    12-13   457: 1-4 ,[object Object]
Day Two ,[object Object],[object Object],[object Object],[object Object],[object Object]
Overlapping Triangles ,[object Object],A C B A F E
Is  ABC similar to  AEF? If so, what Is the missing side? y 15 16 x 12 12 A B C E F
It often helps to separate the two attached triangles. y 15 16 x 12 12
Prove: A line drawn from a point on one side of a triangle parallel to another side forms a triangle similar to the original triangle.
[object Object],[object Object],WARNING
Given:  ; Prove: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
9. Given:    Prove: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],A E D B C
Overlapping Similar Triangles Theorem ,[object Object],[object Object]
Solve by using proportions 4 ft 6 ft 5 ft x
Assign: 453: 9; 14, 16, 21a, 23, 26  457: 5-7

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8 3 Similar Triangles

  • 1. Similar Triangles Focus – Apply the properties of similar triangles and tomorrow, prove that triangles are similar. Lesson 8-3 WA State Standards: G.3.A and G.3.B
  • 2. Congruent Triangles …have matching angles that are congruent. …have matching sides that are congruent. A B C D F E 100° 35° 45° 115 ft 150 ft 100 ft 150 ft 115 ft 100 ft 35° 100° 45°
  • 3. Congruent Triangles …have matching angles that are congruent. …have matching sides that are congruent. A B C D F E 100° 35° 45° 115 ft 150 ft 100 ft 150 ft 115 ft 100 ft 35° 100° 45°
  • 4.
  • 5.
  • 6.
  • 7.
  • 8. Are they similar? Use Angle/Angle or AA Similarity . Two congruent angles show triangles are similar.
  • 9.
  • 10. Is ABC similar to AEF? A E F C B Sometimes it helps to separate the two triangles and look at each angle separately.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16. Is ABC similar to AEF? If so, what Is the missing side? y 15 16 x 12 12 A B C E F
  • 17. It often helps to separate the two attached triangles. y 15 16 x 12 12
  • 18. Prove: A line drawn from a point on one side of a triangle parallel to another side forms a triangle similar to the original triangle.
  • 19.
  • 20.
  • 21.
  • 22.
  • 23. Solve by using proportions 4 ft 6 ft 5 ft x
  • 24. Assign: 453: 9; 14, 16, 21a, 23, 26 457: 5-7