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

2. Can we Prove? ABC ~ BDC~ ADC
Given:

3. Geometry
• Geometric Mean
• Short Leg
• Long Leg
• Hypotenuse

4. • The geometric mean of two
numbers x and y is the
positive number m such that
x m
, so m xy
m y

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

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

7. Altitude to Hypotenuse

8. Altitude to Hypotenuse

9. Altitude to Hypotenuse
• The altitude extending
from the hypotenuse to the
right angle.

10. 21
a hh b
1 d e 2
c

11. Example
c
a b
d

12. Example
d
c d
a c c
b
a b
d

13. Example
c
a b
d

14. Example
d
c d
a c c
b
a b
d

15. Example
c
a b
d

16. Example
d
c d
a c c
b
a b
d

17. Example
c
a b
d

18. Example
d
c d
a c c
b
a b
d

19. Example
c
a b
d

20. Example
d
c d
a c c
b
a b
d

21. Example
c
a b
d

22. Example
d
c d
a c c
b
a b
d

23. Example
c
a b
d

24. Example
d
c d
a c c
b
a b
d

25. Example
c
a b
d

26. Example
d
c d
a c c
b
a b
d

27. 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.

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

29. 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.

30. • d h
=
h e
h
d e

31. •Long-Long, Short-Short
d h
=
h e
h
d e

32. • Long-Long, Short-Short
• The ratio of the longer legs is
equal to the ratio of the
shorter legs d h
=
h e
h
d e

33. •Solve for x:
9
x
5

34. Example
x
5 8
5=x x=?
x 8

35. 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.

36. Example
b
h
d e
d+e=b
b e

37. Example
2
x
3 1
3 +1 = 2
2 1

38. Classwork
•Practice 10-3 odds

39. 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.