Multiplication Division Properties Lesson 2 6 Theorem 14

Theorem 14: If segments or angles are congruent, then their like multiples are congruent.

B, C and F, G are trisection points on two segments AD and EH

Theorem 15: If two segments or angles are congruent, then their like divisions are

Multiplication and Division Proofs: 1. Look for a double use of the word midpoint,

Given: <CAT is congruent to <DOG Ray AT and ray AK trisect <CAR Ray

What property will you use? Write your proof. 1. CAT is to DOG 2.

Slides: 9

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Multiplication & Division Properties Lesson 2. 6

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: 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 <DOP Prove: <CAR is congruent to < DOP 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. 1. CAT is to DOG 2. AT and AK trisect CAR 3. OG and OF trisect DOP 1. Given 2. Given 3. Given 4. CAT TAK KAR 4. If 2 rays trisect an , they divide it into 3 s. 5. DOG GOF FOP 5. Same as #4 6. Multiplication Property 6. CAR DOP