Transcript Medians of Similar Triangles

D. N. A.
1) Use the figure to complete the proportions.
V
P
U
Q
T
a)
R
b)
S
c)
2) Solve for x.

UT
QR
TS
PR
US

PQ
UT
VQ
VT

QR
12
x2
PQ
TS
13
x
d)
VR
VS

PQ
UT
Chapter 7-5
Parts of Similar Triangles
Five-Minute Check (over Lesson 7-4)
Main Ideas
California Standards
Theorem 7.7: Proportional Perimeters Theorem
Example 1: Perimeters of Similar Triangles
Theorems: Special Segments of Similar Triangles
Example 2: Write a Proof
Example 3: Medians of Similar Triangles
Example 4: Solve Problems with Similar Triangles
Theorem 7.11: Angle Bisector Theorem
Standard 4.0 Students prove basic theorems
involving congruence and similarity. (Key)
• Recognize and use proportional relationships of
corresponding perimeters of similar triangles.
• Recognize and use proportional relationships of
corresponding angle bisectors, altitudes, and
medians of similar triangles.
Proportionate Perimeters of Polygons
(try saying that 10 times fast—quietly!!!)
• If two polygons are similar, then
A
the ratio of their perimeters is
equal to the ratios of their
15
corresponding side lengths.
6  9  12  15
4  6  8  10
6
B
9
3
C
12

42
28

3
2
D
4
W
10
X
Y
6
2
Z
8
Perimeters of Similar Triangles
Perimeters of Similar Triangles
Proportional
Perimeter Theorem
Substitution.
Cross products
Multiply.
Divide each side
by 16.
A.
B.
C.
D.
Similar Triangle Proportionality
• If two triangles are similar, then the ratio of any two
corresponding lengths (sides, perimeters, altitudes,
medians and angle bisector segments) is equal to the
scale factor of the similar triangles.
Example
• Find the altitude QS.
24
N
M
P
NP

TR
3
6
2
24
16

6
x
3 x  12
Q
x4
R
S
16

T
3
2
A.
B.
C.
D.
Medians of Similar Triangles
Medians of Similar Triangles
Write a proportion.
EG = 18, JL = x, EF = 36, and JK = 56
Cross products
Divide each side by 36.
Answer: Thus, JL = 28.
A. 2.8
B. 17.5
C. 3.9
D. 0.96
1.
2.
3.
4.
A
B
C
D
Solve Problems with Similar Triangles
Solve Problems with Similar Triangles
Solve Problems with Similar Triangles
Write a proportion.
Cross products
Simplify.
Divide each side by 80.
Answer: The height of the pole is 15 feet.
A. 10.5 in
B. 61.7 in
C. 21 in
D. 28 in
Triangle Bisector Theorem
• If a ray bisects an angle of a triangle, then it divides
the opposite side into segments whose lengths are
proportional to the lengths of the other two sides.
If CD bisects ACB, then
AD
DB

CA
A
CB
D
C
B
Example #3
Find DC
AD bisects BAC
Triangle Bisector Thm.
9

15
14  x
x
9 x  15(14  x)
9 x  210 15x
24 x  210
B
9
14-x
A
D
14
x
15
C
x
210
24

35
4
1) Find the perimeter
of
2) Find the perimeter
 JKL if  JKL ~  RST.
10
R
T
14
 DEF if  DEF ~  ABC.
C
25
F
15
A
D
16
27
E
B
L
12
14
S
J
of
K
3) Find FG if  JKL ~  RST, SH is an altitude
of  RST , FJ is an altitude
of  EFG ,
F
ST  6, SH  5, and FJ  7.
S
R
H
T
E
J
G
Homework
Chapter 7-5
Pg 419
1-13 skip #3, 19-22,
25-26, 39-40