1. GT Geometry Drill 3/7/14
Turn in HW on the bookshelf
What is the geometric mean of
the two measurements?

2. GT Geometry Drill 3/7/14
Turn in HW on the bookshelf
What is the geometric mean of
the two measurements?
1) 2 and 8
2) 16 and 1
3) 12 and 2

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

4. Altitude to Hypotenuse

5. Altitude to Hypotenuse

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

7. 21
hh b
a
1
d
e 2
c

8. Example
c
a
d
b

9. Example
d
d
c
a
c
c
b
a
d
b

10. Example
c
a
d
b

11. Example
d
d
c
a
c
c
b
a
d
b

12. Example
c
a
d
b

13. Example
d
d
c
a
c
c
b
a
d
b

14. Example
c
a
d
b

15. Example
d
d
c
a
c
c
b
a
d
b

16. Example
c
a
d
b

17. Example
d
d
c
a
c
c
b
a
d
b

18. Example
c
a
d
b

19. Example
d
d
c
a
c
c
b
a
d
b

20. 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.

21. Solve for x
x
6
3

22. Solve for x
x
8
4

23. 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.

24. •
d
h
=
h
e
h
d
e

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

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

27. •Solve for x:
9
5
x

28. Example
x
5
5=x
x 8
8
x=?

29. 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.

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

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

32. Classwork
•Assignment #78

33. Conclusion
• 1) A right triangle can be
divided by its altitude so
that…
• 2) In your own words, state
what Long-Long, ShortShort means.