GeometryProof-1(Basic Proportionality Theorem)
In this section we will discuss geometryproof-1 which contains the proofs on basic proportionality theorems.
If the two lines are parallel then their intercepts are in proportion.
3) If DE || AQ and DE || AR. Prove that EF || QR.
Given : DE || OQ and DF || OR
Prove that : EF || QR.
Proof :
Statements |
Reasons |
1) DE || OQ |
1) Given (ΔPOQ) |
3) PE/EQ = PD/DO |
3) Basic Proportionality Theorem |
4) DF || OR |
4) Given (ΔPOR) |
5) PF/FR = PD/DO |
5)Basic Proportionality Theorem |
6) PE/EQ = PD/DO |
6) From (2) and (4) (Transitivity) |
7) EF || QR |
7) Converse of Basic Proportionality Theorem |
GeometryProof1
4) Given : A, B and C are the points on OP,OQ and OR respectively such that AB || PQ and AC || PR.

Given: AB || PQ and AC || PR.
Prove that : BC || QR
Proof :
Statements |
Reasons |
1) AB || PQ |
1) Given (ΔOPQ) |
3) OA/AP = OB/BQ |
3) Basic Proportionality Theorem |
4) AC || PR |
4) Given (ΔOPR) |
5) OA/AP = OC/CR |
5)Basic Proportionality Theorem |
6) OB/BQ = OC/CR |
6) From (2) and (4) (Transitivity) |
7) BC || QR |
7) Converse of Basic Proportionality Theorem |
5) In given figure, DE || BC and CD || EF. Prove that AD
2 = AB x AF

Given : DE || BC and CD || EF
Prove that : AD
2 = AB x AF
Proof :
Statements |
Reasons |
1) DE || BC |
1) Given (ΔABC) |
3) AB/AD = AC/AE |
3) Basic Proportionality Theorem |
4) FE || DC |
4) Given (ΔADC) |
5) AD/AF = AC/AE |
5)Basic Proportionality Theorem |
6) AB/AD = AD/AF |
6) From (2) and (4) (Transitivity) |
7) AD2 = AB x AF |
7) Cross multiply |
•
Geometry proofs
• GeometryProof-1
• GeometryProof 2
• Proofs on Area of similar triangles
• Pythagorean theorem
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