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Stay Home , Stay Safe and keep learning!!!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.
| Given : ΔABC, P is the mid point of AB and
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|
| 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)|
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