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GT Geom. DRILL 1/10/12 SIMPLIFY( exact answers) 1) (√7)(√6) 2)4√ 5 – 2√5 3) 5 4) 3√2 + 5√2

005 30 60-90, 45-45-90

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Page 1: 005 30 60-90, 45-45-90

GT Geom. DRILL 1/10/12

SIMPLIFY( exact answers)

1) (√7)(√6) 2)4√ 5 – 2√5

3) 5 4) 3√2 + 5√2

√10

Page 2: 005 30 60-90, 45-45-90

objectiveSTW continue to work with the Pythagorean theorem and special right triangles

Page 3: 005 30 60-90, 45-45-90

THINK! In an isosceles right triangle the

length of one leg is 5cm find the other two sides of a triangle.

In an equilateral triangle the sides measure 6 cm find the height and then find the area.

Page 4: 005 30 60-90, 45-45-90

TheoremIn a 45-45-90 triangle , the hypotenuse is √2 times the length of a leg.

Page 5: 005 30 60-90, 45-45-90

45-45-90 triangle

x

x x√2

45

45

Page 6: 005 30 60-90, 45-45-90

TheoremIn a 30-60-90 triangle, the

hypotenuse is twice as long as the shorter leg, and the longer leg is √3 times as long as the shorter leg.

Page 7: 005 30 60-90, 45-45-90

30-60-90 triangle

x

2xx√3

30

60

Page 8: 005 30 60-90, 45-45-90

Find z and y

z

y345 8y

30

z

6y45

zz

y60

38

Page 9: 005 30 60-90, 45-45-90

Find z and y

z

y345

2

904545

xc

xb

xa

232

3

3

904545

xc

xb

xa

Page 10: 005 30 60-90, 45-45-90

Find z and y

xc

xb

xa

2

3

906030

82

3

906030

xc

xb

xa8y

30

z

82

343

4

906030

xc

xb

xa

Page 11: 005 30 60-90, 45-45-90

Find z and y

z

y60

38

Page 12: 005 30 60-90, 45-45-90

Find z and y

6y45

z

Page 13: 005 30 60-90, 45-45-90

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