9.4 proportional parts and triangles

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