Worth 20 points if answered correctly. given: △abc, bd¯¯¯¯¯ bisects ∠abc prove: ad/dc = ab/bc statements reasons 1 △abc , bd¯¯¯¯¯ bisects ∠abc given 2 ∠aeb≅∠dbc (section a.) 3 ∠dbc≅∠abd definition of bisector 4 ∠aeb≅∠abd transitive property 5 ∠abd≅∠bae alternate interior angles theorem 6 ∠aeb≅∠bae (section b.) 7 ab = eb converse of isosceles base angle theorem 8 ad/dc = eb/bc (section c.) 9 ad/dc = ab/bc substitution property answer options: 1. transitive property 2. corresponding angles theorem 3. triangle proportionality theorem 4. alternate exterior angles theorem 5. angle addition postulate note: pick the answer number for which section it belongs to.

Given: △ABC,  segment BD bisects ∠ABC

StatementsReasons

1 △ABC , segment BD bisects ∠ABC(Given )

2 ∠AEB≅∠DBC seg (AE) ║seg DB so by Corresponding Angles Theorem    

3 ∠DBC≅∠ABD Definition of bisector

4∠AEB≅∠ABD  Transitive Property

5∠ABD≅∠BAEAlternate Interior Angles Theorem

6∠AEB≅∠BAE     Transitive Property  (If a = b and b = c then a =c)

7AB = EB Converse of Isosceles Base Angle Theorem

8 AD/DC = EB/BC Triangle Proportionality Theorem

9 AD/DC = AB/BC Substitution Property

Step-by-step explanation:

We have been given a sum . We are asked to rewrite this sum using distributive property and greatest common factor.

First of all, we will find greatest common factor of 72 and 60.

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

We can see that the greatest common factor of 72 and 60 is 12.

We can rewrite our given sum as:

Upon factoring out 12, we will get:

Therefore, our required expression is .