8 1 similarity in rt tri

Right TrianglesRight Triangles

8-1 Similarity in Right Triangles8-1 Similarity in Right Triangles

ReviewReview

a

b d

c= MeansExtremes Means

Geometric MeanGeometric Mean

a

x b

x=

The geometric mean between a and b is x if you do this:

What is x?

x ab=

What is the geometric mean What is the geometric mean between 2 and 18?between 2 and 18?

1. 9

2. 6

3. 20

4. 8

0

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2019181716151413121110987654321

TheoremTheorem

• If the altitude is drawn to the hyp. of a right triangle, then the two triangles formed are similar to the original triangle and to each other.

CorollaryCorollary

• The length of the altitude is the geometric mean between the segments of the hypotenuse

Corollary 2Corollary 2

• Each leg is the geometric mean between the hyp. And the segment of the hyp. that is adjacent to that leg

u is the geometric mean between u is the geometric mean between __ and __.__ and __.

u

k

t v

sr

1. s,r

2. k,r

3. k,s

4. v,u

5. t,r

0

2524232221

2019181716151413121110987654321

t is the geometric mean between __ t is the geometric mean between __ and __.and __.

u

k

t v

sr

0

1. s,r

2. k,r

3. k,s

4. t,u

2524232221

2019181716151413121110987654321

v is the geometric mean between v is the geometric mean between __ and __.__ and __.

u

k

t v

sr

0

1. s,r

2. k,r

3. k,s

4. t,v

2524232221

2019181716151413121110987654321

v is the geometric mean between v is the geometric mean between __ and __.__ and __.

u

k

t v

sr

1. s,r

2. k,r

3. k,s

4. t,v

2524232221

2019181716151413121110987654321

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