Beginners Guide to TikTok for Search - Rachel Pearson - We are Tilt __ Bright...
Geometry
1. Altitude and Hypotenuse of Right
Triangles
TAGUPA, Kristian A.
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
2. Lets call this altitude BD.
We start with ΔABC.
B
A
D C
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
3. This divides the triangle into 2
A
smaller triangles. B
A
D C
A D C
ΔADB Band ΔBDC C
are formed.
ΔABC ΔADB ΔBDC
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
4. THEOREM
The altitude to the
hypotenuse of a right triangle
forms two triangles that are
similar to the original.
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
5. Let’s investigate!
A
From ΔBDC ΔADB
we have
B
D C D B
Geometric
P: 555.123.4568 F: 555.123.4567
|
123 West Main Street, New York, www.rightcare.com
NY 10001
Mean
6. The altitude to the
hypotenuse is the
geometric mean between
the segments into
which it separates the
hypotenuse.
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
7. Corollary 1
In any right triangle, the altitude to
the hypotenuse is the geometric mean
between the segments into which it
separates the hypotenuse.
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
8. Let’s investigate!
Let’s investigate!
A
A From ΔABC
ΔACB, we have
D
B C D B
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
9. AB is the geometric
mean of the hypotenuse
(AC) and the segment
of the hypotenuse
adjacent to AB.
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
10. Let’s investigate!
A
A
D
B C D B
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
11. Let’s investigate!
Let’s investigate!
A
From ΔBDC
ΔABC, we have
B
D
D C B C
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
12. BC is the geometric
mean of the hypotenuse
(AC) and the segment
of the hypotenuse
adjacent to BC.
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
13. Let’s investigate!
A
B
D
D C B C
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
14. Corollary 2
In any right triangle, each leg is a
geometric mean of the hypotenuse and
the segment of the hypotenuse adjacent
to the leg.
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
15. Let’s investigate further!
By Corollary 1,
x
c
a
y
h
b P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York, | www.rightcare.com
NY 10001
16. Given: Right ΔTRI with altitude RM.
a. If IM = 16 and RM = 8. Find TM.
By Corollary 1, I
16x = 64 M
x = 4
T R
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
17. Given: Right ΔTRI with altitude RM.
a. If IT = 25 and TM = 5. Find RM.
By Corollary 1, I
(RM)2 = 100
M
RM = 10
T R
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
18. Let’s investigate further!
By Corollary 2,
x
c
a
y
h
b P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York, | www.rightcare.com
NY 10001
19. Let’s investigate further!
By Corollary 2,
x
c
a
y
h
b P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York, | www.rightcare.com
NY 10001
20. Given: Right ΔTRI with altitude RM.
a. If IT = 12 and TM = 3. Find TR.
By Corollary 2, I
(TR)2 = 36 M
TR = 6
T R
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
21. Practice Exercise:
Solve for the unknowns.
The given triangle is a right
triangle.
4
a 8
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
22. Practice Exercise:
Solve for the unknowns.
The given triangle is a right
triangle.
b
5 15
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
23. Assignment
Solve for the unknowns.
The given triangle is a right
triangle.
4
l 36
h
g P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
24. THANK YOU!
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
25. GEOMETRIC MEAN
Definition
If a, b, c are positive numbers, and
Then, b is called the geometric mean
between a and c.
P: 555.123.4568 F: 555.123.4567
123 West Main Street, New York,
NY 10001
| www.rightcare.com
