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In the given figure LM parallel to CB and LN parallel to CD prove that AM /AB= AN/AD
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In the given figure LM parallel to CB and LN parallel to CD prove that...
Thales Theorem and Its Application

Thales Theorem, also known as the Basic Proportionality Theorem, states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. In other words, if a line is drawn parallel to one side of a triangle, it forms several smaller triangles that are similar to the original triangle.

Given Information:
- In the given figure, LM is parallel to CB and LN is parallel to CD.
- We need to prove that AM / AB = AN / AD.

Proof:

Step 1: Establishing the Similarity of Triangles

To prove the given statement, we can start by establishing the similarity of triangles. Let's consider triangle ABC and triangle LAM.

- LM is parallel to CB (given)
- Therefore, by the Thales Theorem, triangle LAM is similar to triangle ABC.

Similarly, considering triangle ACD and triangle LNA:

- LN is parallel to CD (given)
- Hence, by the Thales Theorem, triangle LNA is similar to triangle ACD.

Step 2: Using the Property of Similar Triangles

Since triangles LAM and ABC are similar, we can write the following proportion:

AM / AB = LM / CB ...(1)

Similarly, since triangles LNA and ACD are similar, we have:

AN / AD = LN / CD ...(2)

Step 3: Substituting the Given Information

From the given information, we know that LM is parallel to CB, and LN is parallel to CD. Therefore:

LM / CB = LN / CD

Substituting this equation into equation (1), we get:

AM / AB = LN / CD

Similarly, substituting this equation into equation (2), we have:

AN / AD = LN / CD

Step 4: Conclusion

From equations (3) and (4), we can conclude that AM / AB = AN / AD. Thus, the given statement is proved.

Hence, the ratio of the lengths AM to AB is equal to the ratio of the lengths AN to AD.
Community Answer
In the given figure LM parallel to CB and LN parallel to CD prove that...
Hey see..

given that :- LM//CB

LN//CD

to prove:- AM/AB = AN/AD

proof :- we know that LNM and CBD are straight line

so that . MN//BD

therefore the give figure is a parallelogram so that

MN//LC//BD

so , we know that a Line parallel to one its also parallel to other in a parallelogram

therefore AM =AN

and. AB = AD

so that

AM/AB = AN/AD proved

hope you get helped

thanks
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