Right tri sim day 1

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Drill 3/4/13 •Solve for x: •1) 3) •2) 4 x = x 9 3 x = x 12 4 x = x 12

Transcript of Right tri sim day 1

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Drill 3/4/13•Solve for x:•1) 3)

•2)

4x

= x9

3x

= x12

4x

= x12

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Given:

Can we Prove? BDC ADCABC ~ ~

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Geometry

• Geometric Mean• Short Leg• Long Leg • Hypotenuse

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• The geometric mean of two numbers x and y is the positive number m such that

xymsoym

mx

,

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• Find the geometric mean between:• 1) 4 and 9• 2) 3 and 6• 3) 8 and 12

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Objective•Students will explore the properties of similar right triangles so that they can find unknown sides.

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Altitude to Hypotenuse

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Altitude to Hypotenuse

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Altitude to Hypotenuse• The altitude extending

from the hypotenuse to the right angle.

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1

12

2d e

ha b

c

h

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Example

a bd

c

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Example

a bd

cd

da cc

b

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Example

a bd

c

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Example

a bd

cd

da cc

b

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Example

a bd

c

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Example

a bd

cd

da cc

b

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Example

a bd

c

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Example

a bd

cd

da cc

b

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Example

a bd

c

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Example

a bd

cd

da cc

b

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Example

a bd

c

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Example

a bd

cd

da cc

b

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Example

a bd

c

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Example

a bd

cd

da cc

b

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Example

a bd

c

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Example

a bd

cd

da cc

b

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Right ∆ Similarity Theorem• The altitude to the hypotenuse

of a right triangle divides the triangle into 2 triangles that are similar to each other and the original triangle.

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Write all the proportions you can think of comparing the corresponding sides of the triangles.

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Corollary 1• The length of the altitude to

the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.

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h

d e

dh

= he

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•Long-Long, Short-Short

h

d e

dh

= he

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• Long-Long, Short-Short• The ratio of the longer legs is

equal to the ratio of the shorter legs

h

d e

dh

= he

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•Solve for x:

x5

9

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Example

5 8

x

5 = xx 8 x = ?

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Corollary 2• The altitude to the hypotenuse of a

right triangle intersects it so that the length of each leg is the geometric mean of the length of its adjacent segment of the hypotenuse and the length of the entire hypotenuse.

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Example

d e

hb

d + e = bb e

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Example

3 1

x2

3 +1 = 22 1

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Classwork•Practice 10-3 odds

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Conclusion• 1) A right triangle can be

divided by its altitude so that…• 2) In your own words, state

what Long-Long, Short-Short means.