Page 130 - Math Course 3 (Book 2)

Proportional Parts of Triangles
Mo. 10

Lesson 4 COROLLARIES

10.1 If three or more parallel lines intersect two
transversals, then they cut off the transver-
KEY CONCEPTS:
sals proportionally.
1. Use proportional parts of triangles. AB DE
↔ ↔ ↔
2. Divide a segment into parts. Example: If DA || EB || FC, then =
BC EF
AB = DE and AC = DF
BC EF BC EF

MO. 10 - L4a 7.2 If three ore more parallel lines cut off
congruent segments on one transversal,
Using Proportional Parts of then they cut off congruent segments on
every transversal.
Triangles

Example: If AB ≅ BC, then DE ≅ EF.
THEOREM 10.4 F

Triangle Proportionality Theorem E

If a line is parallel to one side of a triangle and D
intersects the other two sides in two distinct
points, then it separates these sides into segments
of proportional lengths.
BA DE A
Example: If BD || AE, =
CB CD
B
C
C

B D
Let’s Begin

A E
Find the Length of a Side
THEOREM 10.5 Example

Converse of the Triangle Proportional

If a line intersects two sides of a triangle and In △RST, RT || VU, SV = 3, VR = 8, and UT = 12.
separates the sides into corresponding segments Find SU.
of proportional lengths, then the line is parallel to
the third side. R 8 V 3

Example: BA = DE , then BD || AE. S
CB CD
x
C
U

B D
12
E
A T
122