The two-column proof with missing statements and reasons proves that if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally.

Complete the proof by entering the correct statements and reasons.

Question

The two-column proof with missing statements and reasons proves that if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally. 



Complete the proof by entering the correct statements and reasons.

anonymous · Answer

@Hero

anonymous · Answer

Here is the new question

anonymous · Answer

@Hero The entire question altogether is in the picture

anonymous · Answer

@Hero are you there? :)

hero · Answer

I have some ideas for it, but I'm not sure I should give them away.

anonymous · Answer

@Hero I just need help with figuring out which statement goes into the #3

hero · Answer

When you have two parallel lines cut by a transversal, what useful relationships are known as a result?

anonymous · Answer

@Hero you can use the relationships between angles

directrix · Answer

@iluvmath  What is odd to me is that the reason for the last statement of the proof is "Converse of the SSS Similarity Theorem." I would have expected "Corresponding sides of similar triangles are in proportion." 

You can get the triangles similar by the AA Postulate.

hero · Answer

Directrix, you revealed one of the reasons of a statement from the proof that hasn't been added yet

anonymous · Answer

@Hero I am not sure of which statement goes where?

hero · Answer

You know that for the third statement, it will be something involving showing angles congruent. for the fifth statement, it will be showing something regarding AA Postulate .

anonymous · Answer

@Hero so would the 5th statement would it be the angel angle postulate or wound tht be the reason

directrix · Answer

@Hero At this point, I am not so sure of that. I do now think that the converse of the Side-Side-Side Similarity Theorem could be thought of as being equivalent to "Corresponding sides of similar triangles are in proportion." The task is to get the triangles similar.

hero · Answer

We're already given one of the angles from both triangles congruent:

$$\angle{b} \cong \angle{b}$$

We only need to show one more set of angles congruent in order to use AA Similarity Postulate. 

I agree it is kind of weird because they want us to use SSS Similarity Postulate. So, I get what you mean.

anonymous · Answer

@Hero so i dont understand what the 5th statement eould be

anonymous · Answer

@hero okay i understand it now thank you for your help sir :-)))