In any triangle PQR, K and M are the mid-points of PQ and QR respectively. If E be any point on the side PR and KE//QR. Prove that: QK = ME.
In any triangle PQR, K and M are the mid-points of PQ and QR respectively. If E be any point on the side PR and KE//QR. Prove that: QK = ME.
Given,
- PK = KQ
- QM = MR
- KE // QR
To Prove: QK = ME
Proof:
- KE bisects PR (Line passing through the midpoint of any one side of a triangle, (PR in this case) and parallel to the third side(KE//QR, in this case), bisects the third side)
- ME = PQ/2 (Line joining the mid points, M and E(in this case), of any two sides of a triangle, QR and MR(in this case), is half of and parallel to the third side)
- QK = PQ/2 (K is the mid-point of PQ)
- QK = ME (From 2 and 3)
