GeometryProof-1(Basic Proportionality Theorem)

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

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 AD2 = AB x AF

Given : DE || BC and CD || EF
Prove that : AD2 = 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

Home

Russia-Ukraine crisis update - 3rd Mar 2022

The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.