Download 5.9—Proportions and Similar Triangles Objective

5.9—Proportions and Similar Triangles
Write the following biconditional as a conditional statement and its converse.
Then determine whether it is true or false.
Two angles are supplementary if and only if they form a linear pair.
True or
False
Conditional:________________________________________________________
__________________________________________________________________
Converse:
__________________________________________________________________
__________________________________________________________________
5.9—Proportions and Similar Triangles
calculate
Objective: Use proportionality theorems to ____________________
lengths
segment ___________________________.
Triangle Proportionality Theorem:
parallel
intersects
If a line _____________
to one side of a triangle ______________
the other two sides, then it divides the two sides
________________________.
proportionally
RT RU
If TU || QS , then
R
TQ

US
Converse of the Triangle Proportionality Theorem:
divides
If a line ___________________
two sides of a triangle
proportionally, then it is parallel to the
__________________
__________________.
third
side
R
RT
RU
Examples: Find the value of each variable.
1.
Examples: Find the value of each variable.
2.
Examples: Find the value of each variable.
3.
Theorem:
three parallel lines intersect
If ________
________
transversals, then they
two
divide
______________
the
transversals proportionally.
t
Z
If r || s || t , then
UW
WY

VX
XZ
Examples: Use the figure to complete the proportion.
1.
AB ?

CB ?
3.
GF ?

GE ?
2.
CD ?

AD ?
4.
GF ?

ED ?
5. Use the diagram to find LM and MN to the nearest tenth.
Theorem:
ray bisects an angle of a triangle, then it divides
If a ______
the _____________
side into segments whose lengths are
opposite
proportional to the __________
of the other two sides.
lengths
AD CA

If CD bisects ACB , then
DB CB
Examples: Find the value of x.
5.
Examples: Find the value of x.
6.
Examples: Find the value of x.
7.