Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the...
-
Upload
homer-cameron -
Category
Documents
-
view
218 -
download
1
Transcript of Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the...
Use Similar Right Triangles
Ch 7.3
Similar Right Triangle Theorem
• If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original right triangle.
How do you names the 3 similar triangles?
1. Draw the smallest triangle.
îSUT ~ îTUR
2. Draw the middle triangle.3. Draw the largest triangle.
~ îSTR
4. Match up the angles.
Name the similar triangles, then find x.îEHG ~ îGHF ~ îEGF
45
3 xGF
GH
EF
EG
5
12
125
x
x
To find x make a ratio of the hypotenuses and the a ratio of 2 proportional legs.
Name the similar triangles and find x.îLKM ~ îMKJ ~ îLMJ
sideLongestnd
Hypotenuse
2
KM
LM
JM
JL
x
5
12
13
6013 x
13
60x
Find x and y.
2172
x
y
222 cba 222 7221 c
25182441 c25625 c
c75
longest
Hypnd2
CD
CB
AC
AB
y
21
72
75
151275 y16.20y
222 7216.20 x
12.69x
Find x.
12
3 x
x
362 x
362 x
6x
longest
Shortestnd2
Find xx
x 4
5
202 x
52
225
45
202
x
Theorem 7.6
• In a right triangle the altitude from the right angle to the hypotenuse divides the hypotenuse into 2 segments.
• The length of the altitude is the geometric mean of the lengths of the 2 segments
DBADCD CD
DB
AD
CD
41682 y
48 x
22 )4(8 x
x464
x16
Finding the length of the altitude
B
C A
D1.Set up a proportion to find
BD.2. Find side AD.3. Plug values into
DBADCD
Finding the length of the altitude.
deSmallestSiTriangleSmallest
HypotenuseTriangleSmallest
deSmallestSiTriangleBig
HypotenuseTriangleBig
x
18
18
30
32430
)18)(18(30
x
x
8.10x
10.8
2.198.1030
19.2
8.102.19 Altitude 4.1436.207
Finding the length of the altitude.
deSmallestSiTriangleSmallest
HypotenuseTriangleSmallest
deSmallestSiTriangleBig
HypotenuseTriangleBig
x
6
6
56
3656
)6)(6(56
x
x
7.2x
2.7
7.107.256
10.7
7.27.10 Altitude 3.589.28
Finding the length of the altitude.
deSmallestSiTriangleSmallest
HypotenuseTriangleSmallest
deSmallestSiTriangleBig
HypotenuseTriangleBig
x
15
15
613
225613
)15)(15(613
x
x
6.9x
9.6
8.136.9613
13.8
6.98.13 Altitude 5.1148.132
Find the amplitude, if these are right triangles. One of these is not a right
triangle
8.5 6.6
not right
Theorem 7.7• In a right triangle, the altitude divides the
hypotenuse into 2 segments.
• The length of each leg of each right triangle is the geometric mean of length of the hypotenuse and a segment of the hypotenuse
ADABAC
DBABCB
Find x and y
4.2512.75
xy
DBABCB
ADABAC
25.417CB5.825.72 CB
75.1217AC7.1475.216 AC
Find x
28x
16x
4x
Find x and y
28
x +2y
DBADCD
ADABAC
282 x162 x
810AC9.880 AC
42 x2x
Find a
Find b
Find x and y
yx|--------- 34 -------------|
30z
16