9.4 proportional parts and triangles lesson
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Transcript of 9.4 proportional parts and triangles lesson
9.4 Proportional Parts and Triangles
Proportional Parts and Triangles
You will learn to identify and use the relationships between proportional parts of triangles.
Nothing New!
Proportional Parts and Triangles
In ΔPQR,
TS
RQ
P
Are ΔPQR and ΔPST, similar?
QRST || and intersects the other two sides of ΔPQR.ST
PST PQR corresponding angles
P P
ΔPQR ~ ΔPST. Why? (What theorem / postulate?)
AA Similarity (Postulate 9-1)
Proportional Parts and Triangles
Theorem 9-4
If a line is _______ to one side of a triangle, and intersects the other two sides, then the triangle formed is _______ to the original triangle.
similarparallel
A
B C
D E
then ,|| DEBCIf ΔABC ~ ΔADE.
Proportional Parts and Triangles
TWS
V
R
Complete the proportion:
?
SR
SW
ST
Since RTVW || , ΔSVW ~ ΔSRT.
SR
SW
STSV
Proportional Parts and Triangles
Theorem 9-5
If a line is parallel to one side of a triangle and intersects the other two sides, then it separates the sides into segments of__________________.proportional lengths
ED
CB
A
CE
AC
BD
ABDEBC then ,|| If
Proportional Parts and Triangles
CB
HG
A
5
3
x + 5x
4
x
BCGH
of value the Find
.|| figure, the In
5
43
xx
534 xx
1534 xx
15x
Proportional Parts and Triangles
10 ft
6 ft
4 ftBrace
Jacob is a carpenter.
Needing to reinforce this roof rafter, he mustfind the length of the brace.
4=
10
4 x
10x = 16
x = 1 3
5ft
4 ft
x
Proportional Parts and Triangles