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Special Right Triangles

Dive into the world of special right triangles, from the classic 3-4-5 triangle to angle properties and Pythagorean Theorem applications. Discover how side lengths and angles interact, solving for unknowns and understanding triangle relationships. Brush up on speed trials and congruence rules while exploring the unique characteristics of these geometric gems.

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Special Right Triangles

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  1. Special Right Triangles

  2. Our First Special Right Triangle Is A 3,4,5 The Hypotenuse Must Be A Multiple Of 5 And The Legs Must Be Multiples Of 3 And 4

  3. Use The Pythagorean Theorem To Find X x x 3 5 5 3 25 + 25 = x² 50 = x² 50 = x 5 2 = x 9 + 9 = x² 18 = x² 18 = x 3 2 = x

  4. Speed Trials 45, 45, 90 7 2 4 2 7 4 4 7 13 2 2 2 2 13 2 13

  5. If 2 Sides Of A Triangle Are Congruent, Then The Angles Opposite Them Are Congruent 45 45, 45, 90 | 45 |

  6. 45, 45, 90 Legs are equal Leg x 2 = hyp 45 X 2 | X 45 | X Mult by 2

  7. 8 2 2 2 = 8 2 2 4 2 4 2 = 8 2 Going Backwards….DIVIDE 8 4 2 45 Div by 2

  8. 30, 60, 90 Triangles No angles are equal so no sides are congruent 60 Hyp Short Leg 30 Long Leg

  9. 30, 60, 90 Triangles Mult by 2 60 Hyp Short Leg 30 Long Leg

  10. 30, 60, 90 2 x 8 = 16 60 8 30

  11. 30, 60, 90 2 x 5 = 10 60 5 30

  12. 30, 60, 90 60 Hyp Short Leg 30 Long Leg Mult by 3

  13. 30, 60, 90 60 Hyp 15 30 15 x 3 = 15 3

  14. 30, 60, 90 60 Hyp 3 30 3 x 3 = 3 3

  15. Going Backwards….DIVIDE 13 60 13 2 H SL 30 LL For now, we’ll leave it as an improper fraction

  16. Going Backwards….DIVIDE 60 5 3 = 5 H SL 3 30 LL 5 3

  17. 8 3 3 3 Going Backwards….DIVIDE 8 3 60 H 3 SL 30 LL 8 8 3 = 3

  18. 10 3 3 9 3 2 9 2 5 3 3 30, 60, 90 12 9 5 30 30 30 6 3 6

  19. What Do You Know About This Triangle? 60 30 30 | | 60 60 |

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