Question

class 10 maths Q, PLEASE HELP​

Answer 1

$\begin{gathered}\begin{gathered}\bf \: Given \: - \: \begin{cases} &\sf{LM \: \parallel \: CB} \\ &\sf{LN \: \parallel \:CD} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: To \: prove \: - \: \begin{cases} &\sf{\dfrac{AM}{AB} = \dfrac{AN}{AD} }  \end{cases}\end{gathered}\end{gathered}$

Concept Used :-

Basic Proportionality Theorem

• Statement: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.

$\large\underline\purple{\bold{Solution :- }}$

Now,

$\rm : \implies \:In \: \triangle \: ABC,$

$\rm : \implies \:LM \: \parallel \:CB$

Using Basic Proportionality Theorem, we have

$\boxed{ \pink{\rm : \implies \:\dfrac{AM}{AB} = \dfrac{AL}{AC}}} - - (i)$

Now,

$\rm : \implies \:In \: \triangle \: ADC,$

$\rm : \implies \:LN \: \parallel \:CD$

Using Basic Proportionality Theorem, we have

$\boxed{ \pink{ \rm : \implies \:\dfrac{AL}{AC} \: = \: \dfrac{AN}{AD}}} \: - - (ii)$

From equation (i) and equation (ii), we get

$\boxed{ \red{ \rm : \implies \:\dfrac{AM}{AB} \: = \: \dfrac{AN}{AD}}}$

$\large{\boxed{\boxed{\bf{Hence, Proved}}}}$

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Explore more :-

1. Area Ratio Theorem

• Theorem: If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

2. Pythagoras Theorem

• Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse.

3. Converse of Pythagoras Theorem

• The converse of Pythagoras theorem states that “If the square of a side is equal to the sum of the square of the other two sides, then triangle must be right angle triangle”

4. Converse of Basic Proportionality Theorem

• According to this theorem, if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.