WARM UP Given ST is congruent SM Given ST is congruent SM TP is congruent MN TP is congruent MN Prove SP is congruent SN Prove SP is congruent SN If congruent segments are added to congruent segments, the resulting segments are congruent! 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)

Multiplication and Division Proofs: Multiplication and Division Proofs: 1. Look for a double use of the word midpoint, trisection, bisect in the given information 2. Multiplication Property is used when the segments or angles in the conclusion are greater than those in the given information. 3. Division Property is used when the segments or angles in the conclusion are smaller than the given information.

Given: <CAT is congruent to <DOG Ray AT and ray AK trisect <CAR Ray OG and ray OF trisect <DOE Prove: <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 T C A K R D O G F P

What property will you use? Write your proof Write your proof <CAT is congruent to <DOG Given Ray AT and ray AK trisect <CAR Given Ray OG and ray OF trisect <DOE Given <1 congruent to <2 congruent <3 If 2 rays trisect an angle, then they divide the < into 3 congruent <s <4 congruent to <5 congruent < 6 same as 4 < CAR congruent to < DOEMultiplication Property