2. Proportional Parts and Triangles
You will learn to identify and use the relationships between
proportional parts of triangles.
Nothing New!
3. 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)
4. 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.
similar
parallel
A
B C
D E
then,|| DEBCIf ΔABC ~ ΔADE.
5. Proportional Parts and Triangles
TWS
V
R
Complete the proportion:
?
SR
SW
ST
Since RTVW || , ΔSVW ~ ΔSRT.
SR
SW
ST
SV
6. 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
AB
DEBC then,||If
7. Proportional Parts and Triangles
CB
HG
A
5
3
x + 5x
4
x
BCGH
ofvaluetheFind
.||figure,theIn
5
43
xx
534 xx
1534 xx
15x
8. Proportional Parts and Triangles
10 ft
6 ft
4 ftBrace
Jacob is a carpenter.
Needing to reinforce this roof rafter, he must
find the length of the brace.
4
=
10
4 x
10x = 16
x = 1 3
5
ft
4 ft
x
