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) AD^{2} = AB x AF | 7) Cross multiply |
• Geometry proofs
• GeometryProof-1
• GeometryProof 2
• Proofs on Area of similar triangles
• Pythagorean theorem