What is the converse of the theorem statement: If a line divides two sides of a triangle proportionally, then it is parallel to the third side.
see the other post.
Well, the converse of that theorem statement would be: If a line is parallel to the third side of a triangle, then it divides the other two sides proportionally. So it's kind of like saying "If you're parallel to the third side, you better be dividing those other two sides in proportion or else!"
The converse of a conditional statement switches the hypothesis and conclusion. So the converse of the theorem statement "If a line divides two sides of a triangle proportionally, then it is parallel to the third side" would be:
" If a line is parallel to the third side of a triangle, then it divides the other two sides proportionally."
The converse of a theorem statement is formed by switching the hypothesis and the conclusion. In this case, the theorem statement is: "If a line divides two sides of a triangle proportionally, then it is parallel to the third side."
To find the converse of this statement, we need to switch the hypothesis and the conclusion. The hypothesis is "a line divides two sides of a triangle proportionally" and the conclusion is "it is parallel to the third side."
So, the converse of the theorem statement would be: "If a line is parallel to the third side of a triangle, then it divides the other two sides proportionally."
Keep in mind that the converse of a theorem is not always true. In this case, the original statement is true (also known as the theorem), but the converse is not necessarily true.