What is the converse of the theorem statement: If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
If two sides of a triangle are divided in the same proportion, then the line connecting the dividing points on the sides is parallel to the third side of the triangle.
But how do I write it? Example: is it
A. In triangle QRS, ig RT/TQ=RU/US, then side TU is parallel to side QS.
B. In triangle ABC, if CD=DA and CE=EB,then side DE is parallel to side AB and DE=1/2AB
c. In triangle QRS, if side TU is parallel to side QS, then RT/TQ=RU/US.
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I see that you need help with writing the converse of a theorem statement. To write the converse, we need to switch the "if" and "then" parts of the original statement.
The original theorem statement is: "If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally."
To write the converse, we switch the order and the condition of the statement. The converse is: "If two sides of a triangle are divided in the same proportion, then the line connecting the dividing points on the sides is parallel to the third side of the triangle."
Now, let's examine your options:
A. In triangle QRS, if RT/TQ=RU/US, then side TU is parallel to side QS.
This option seems to have the right idea, but it is not the correct formulation of the converse. It is missing the "two sides divided in the same proportion" condition.
B. In triangle ABC, if CD=DA and CE=EB, then side DE is parallel to side AB and DE=1/2AB.
This option is not the converse because it mentions specific lengths (CD=DA and CE=EB), rather than the general condition of "two sides divided in the same proportion." Also, it introduces a new condition about the lengths of the segments.
C. In triangle QRS, if side TU is parallel to side QS, then RT/TQ=RU/US.
This option correctly states the converse of the original theorem statement. It starts with the condition of the line being parallel, and then states the condition of the sides being divided in the same proportion.
So, the correct option is C. In triangle QRS, if side TU is parallel to side QS, then RT/TQ=RU/US.
Remember, writing the converse means switching the order and condition of the original statement.