Transcript 2.6 Multiplication and Division Properties

WARM UP



Given ST is congruent SM
TP is congruent MN
Prove SP is congruent SN
If congruent segments are added to
congruent segments, the resulting
segments are congruent!
2.6 Multiplication and Division
Properties
Theorem 14: If segments or angles
are congruent, then their like
multiples are congruent. (property of
multiplication.)
B,C and F,G are trisection points on two segments AD and
EH respectfully.
If AB = EF = 3, What can you say about AD and EH?
Draw and label segments
Write a conclusion
Theorem 15: If two segments or angles are congruent,
then their like divisions are congruent. (Property of
division)

1.
2.
3.
Multiplication and Division Proofs:
Look for a double use of the word
midpoint, trisection, bisect in the given
information
Multiplication Property is used when
the segments or angles in the conclusion
are greater than those in the given
information.
Division Property is used when the
segments or angles in the conclusion
are smaller than the given information.




Given:
Ray
Ray
Prove:
<CAT is congruent to <DOG
AT and ray AK trisect <CAR
OG and ray OF trisect <DOE
<CAR is congruent to < DOE
Draw and label
Given: <CAT is congruent to <DOG
Ray AT and ray AK trisect <CAR
Ray OG and ray OF trisect <DOP
Prove: <CAR is congruent to < DOP
C
D
T
G
F
A
K
P
R
O
What property will you use?







Write your proof
<CAT is congruent to <DOG
Ray AT and ray AK trisect <CAR
Ray OG and ray OF trisect <DOE
<1 congruent to <2 congruent <3
<4 congruent to <5 congruent < 6
< CAR congruent to < DOE
Given
Given
Given
If 2 rays trisect an
angle, then they
divide the < into 3
congruent <s
same as 4
Multiplication Property