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Right tri sim day 1
39
Drill 3/4/13 •Solve for x: •1) 3) •2) 4 x = x 9 3 x = x 12 4 x = x 12
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Transcript of Right tri sim day 1
Drill 3/4/13•Solve for x:•1) 3)
•2)
4x
= x9
3x
= x12
4x
= x12
Given:
Can we Prove? BDC ADCABC ~ ~
Geometry
• Geometric Mean• Short Leg• Long Leg • Hypotenuse
• The geometric mean of two numbers x and y is the positive number m such that
xymsoym
mx
,
• Find the geometric mean between:• 1) 4 and 9• 2) 3 and 6• 3) 8 and 12
•
Objective•Students will explore the properties of similar right triangles so that they can find unknown sides.
Altitude to Hypotenuse
Altitude to Hypotenuse
Altitude to Hypotenuse• The altitude extending
from the hypotenuse to the right angle.
1
12
2d e
ha b
c
h
Example
a bd
c
Example
a bd
cd
da cc
b
Example
a bd
c
Example
a bd
cd
da cc
b
Example
a bd
c
Example
a bd
cd
da cc
b
Example
a bd
c
Example
a bd
cd
da cc
b
Example
a bd
c
Example
a bd
cd
da cc
b
Example
a bd
c
Example
a bd
cd
da cc
b
Example
a bd
c
Example
a bd
cd
da cc
b
Example
a bd
c
Example
a bd
cd
da cc
b
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.
Write all the proportions you can think of comparing the corresponding sides of the triangles.
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.
•
h
d e
dh
= he
•Long-Long, Short-Short
h
d e
dh
= he
• Long-Long, Short-Short• The ratio of the longer legs is
equal to the ratio of the shorter legs
h
d e
dh
= he
•Solve for x:
x5
9
Example
5 8
x
5 = xx 8 x = ?
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.
Example
d e
hb
d + e = bb e
Example
3 1
x2
3 +1 = 22 1
Classwork•Practice 10-3 odds
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.
