Geometry Proof 2
In this section we will discuss GeometryProof 2 based on mid point theorem in triangle. If the line joins the mid point of any two sides of a triangle then it is parallel to third side and it one half of the third side.1) In a triangle ABC, P is the mid point of AB, such that PQ  BC.
Given : 1) P is the mid point of AB ⇒ AP = PB.
2) PQ  BC
Prove that : AQ = QC ⇒ Q is the mid point of AC.
Given : ΔABC, P is the mid point of AB and PQ BC Prove that : Q is the mid point of AC. 


1) P is the mid point  1) Given (ΔABC) 
2) AP = PB  2) Definition of mid point 
3) AP / PB = 1  3) Ratio of two equal side is 1. 
4) PQ  BC  4) Given (ΔABC) 
5) ( AP / PB ) = ( AQ / QC )  5) Basic Proportionality Theorem 
6) AQ / QC = 1  6) From (3) and (5) (Transitivity) 
7) AQ = QC  7) Cross multiply 
8) Q is the mid point of AC  8) Definition of mid point 

2) ABCD is a trapezoid in which AB  DC and its diagonals intersect each other at 'O'.
Given : 1) ABCD is a trapezoid. 2) AB  DC Prove that : OE  DC. Construction : Draw OE such that OE DC 


1) OE  DC  1) Construction (ΔABC) 
2) (BO / OD) = ( BE / EC)  2) Basic Proportionality Theorem 
3) AB  DC  3) Given 
4) OE  AB  4) From (1) and (3) (Transitivity) 
5) (AO / CO) = (BE / EC)  5) Basic Proportionality Theorem 
6) (AO / CO) = (BO / DO)  6) From (2) and (5) ( Transitivity) 
7) (AO / BO) = (CO / DO)  7) From above ( Alternendo) 
• Geometry proofs
• GeometryProof1
• GeometryProof 2
• Proofs on Area of similar triangles
• Pythagorean theorem