WARM UP

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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!

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2.6 Multiplication and Division Properties

• Theorem 14 If segments or angles are congruent,
  then their like multiples are congruent.
  (property of multiplication.)

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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
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Theorem 15 If two segments or angles are
congruent, then their like divisions are
congruent. (Property of division)
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• 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.

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• Given ltCAT is congruent to ltDOG
• Ray AT and ray AK trisect ltCAR
• Ray OG and ray OF trisect ltDOE
• Prove ltCAR is congruent to lt DOE

Draw and label
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Given ltCAT is congruent to ltDOG Ray AT and ray
AK trisect ltCAR Ray OG and ray OF trisect
ltDOP Prove ltCAR is congruent to lt DOP
D
C
G
T
F
K
A
P
O
R
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What property will you use?

• Write your proof
• ltCAT is congruent to ltDOG Given
• Ray AT and ray AK trisect ltCAR Given
• Ray OG and ray OF trisect ltDOE Given
• lt1 congruent to lt2 congruent lt3 If 2 rays
  trisect an angle, then they divide
  the lt into 3 congruent lts
• lt4 congruent to lt5 congruent lt 6 same as 4
• lt CAR congruent to lt DOE Multiplication
  Property

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