Question drawn from very renowned book RD sharma of class 10th, Chapter no. 4
Chapter name:- Triangles
Exercise :- 4.2
This is very important question of triangle.
In this question we have three-line segments OA, OB, and OC, and points L, M, N respectively
And they are chosen that in such a way that LM ∥ AB and MN ∥ BC but neither of L, M, and N nor A, B, C are collinear.
Now we have to Show that LN ∥ AC by using triangle geometrical properties.
learning CBSE maths in efficient way
RD sharma, DHANPAT RAI publication
Class 10th, triangle
OA, OB and OC, points are L, M, and N respectively
Such that LM || AB and MN || BC
To prove: LN ∥ AC
In ΔOAB, Since, LM ∥ AB,
Then, OL/LA = OM/ MB (By using BPT) – equation 1
In ΔOBC, Since, MN ∥ BC
Then, OM/MB = ON/NC (By using BPT)
Therefore, ON/NC = OM/ MB – equation 2
From equation 1 and 2, we get
OL/LA = ON/NC
Therefore, In ΔOCA By converse BPT, we get
LN || AC