Opposite sides of a parallelogram are equal Proof of Converse of Midpoint TheoremĭE || BC (given) and BD || CF (by construction) To Prove: E is the midpoint of AC (i.e., AE = CE)Ĭonstruction: Through C, draw a line parallel to AB that meets the extended DE at F. Given: In ΔABC, D is the midpoint of AB and DE || BC. A line through D parallel to BC meets AC at E, as shown below. Proof of Mid Point Theorem ConverseĬonsider a triangle ABC, and let D be the midpoint of AB. We prove the converse of mid point theorem by contradiction. Statement: The converse of midpoint theorem states that "the line drawn through the midpoint of one side of a triangle that is parallel to another side will bisect the third side". Will the converse of the midpoint theorem hold? Yes, it will, and the proof of the converse is presented next. Given: D and E are the mid-points of sides AB and AC of ΔABC respectively.Ĭonstruction: In ΔABC, through C, draw a line parallel to BA, and extend DE such that it meets this parallel line at F, as shown below:īD || CF (by construction) and BD = CF (from 7) Let E and D be the midpoints of the sides AC and AB respectively. Consider the triangle ABC, as shown in the figure below. I.e., in a ΔABC, if D and E are the midpoints of AB and AC respectively, then DE || BC and DE = ½ BC. Statement: The midpoint theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the third side.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |