Assertion: triangle's line | /r/HasProperty | parallel
Facets:
value: to bc
type: LOCATION
value: to a side of the triangle
type: LOCATION
value: to the sides
type: OTHER
Source sentences:
text: The Lemoine hexagon is a cyclic hexagon with vertices given by the six intersections of the sides of a triangle with the three lines that are parallel to the sides and that pass through its symmedian point.
text: This is not true for other lines through the centroid; the greatest departure from the equal-area division occurs when a line through the centroid is parallel to a side of the triangle, creating a smaller triangle and a trapezoid; in this case the trapezoid's area is 5/9 that of the original triangle.
text: The two diagonal lines are parallel, and the area of the region between them is $42$
text: So I'm going to say that these two lines must be parallel, the second key thing about this midsegment is that it's going to be half of the length of the third side.
text: In the diagram shown above, we see triangle ABC and the dotted line through A that is parallel to BC.
text: We also know that since the dotted line is parallel to BC that by alternate interior angles.