Ex 6.2 Q3 - In Fig. 6.18, if LM || CB and LN || CD, prove that AM/AB = AN/AD.
Solution:-Given: LM || CB and LN || CD
To prove:
AM
/
AB
=
AN
/
AD
Proof:
Basic Proportionality Theorem (BPT) states that,
"If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio."
 |
| Fig. 6.18 |
➙ In ∆ABC, LM || CB
∴ By using Basic Proportionality Theorem,
AM
/
MB
=
AL
/
LC
------- ( 1 )➙ In ∆ADC, LN || CD
∴ By using Basic Proportionality Theorem,
AN
/
ND
=
AL
/
LC
------- ( 2 )*From Eqⁿ( 1 ) and ( 2 )
AM
/
MB
=
AN
/
ND
*Reversing the fraction
∴
MB
/
AM
=
ND
/
AN
*Adding 1 on both sides
∴
MB
/
AM
+ 1 =
ND
/
AN
+ 1 ∴
MB + AM
/
AM
=
ND + AN
/
AN
∴
AB
/
AM
=
AD
/
AN
*Reversing the fraction
∴
AM
/
AB
=
AN
/
AD
Hence proved.
------------------------------------
Try This..
✒ In ∆PQR, a line parallel to QR intersects PR and PQ at A and B respectively. Prove that PA/PR = PB/PQ.
✒ In ∆XYZ, if a line parallel to side YZ intersects the other two sides at points A and B, prove that XA/XY = XB/XZ.
❌ Common Mistakes
Forgetting to mention the theorem name:▸ Always write “By Basic Proportionality Theorem”.Mixing up the triangle used for BPT:▸ Make sure you are applying BPT to the correct triangle.Confusing sides:▸ Write ratios correctly: smaller segment over full side.Skipping diagram labeling:▸ Always label the triangle and points clearly for better understanding.Ignoring given conditions:▸ If lines are not parallel, BPT can’t be applied.
Queries Solved:-
Class 10 Ex 6.2
Ex 6.2 Q3 Class 10
Class 10 Ex 6.2 Q3
Class 10 Chap 6 Ex 6.2 Q3
Class 10 Triangles
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