The straight line drawn through the midpoint of one side of a triangle parallel to another bisects the third side.
Given: In ∆PQR, S is the midpoint of PQ, and ST is drawn parallel to QR.
To prove: ST bisects PR, i.e., PT = TR.
Construction: Join SU where U is the midpoint of PR.
Proof:
Statement |
Reason |
1. SU ∥ QR and SU = \(\frac{1}{2}\)QR. |
1. By Midpoint Theorem. |
2. ST ∥QR and SU ∥ QR. |
2. Given and statement 1. |
3. ST ∥ SU. |
3. Two lines parallel to the same line are parallel themselves. |
4. ST and SU are not the same line. |
4. From statement 3. |
5. T and U are coincident points. |
5. From statement 4. |
6. T is the midpoint of PR (Proved). |
6. From statement 5. |
From Converse of Midpoint Theorem to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Dec 06, 23 01:23 AM
Dec 04, 23 02:14 PM
Dec 04, 23 01:50 PM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.