Special Right Triangles

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Presentation transcript:

Special Right Triangles Section 7-3 spi.3.2.G Jim Smith JCHS

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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