In - ABC- BM - AC and CN - AB-Hence- AB-AC - BM-CN - AM-ANIf the above statement is true then mention answer as 1- else mention 0 if false

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Standard IX

Mathematics

Parallel Lines with Transversal

In Δ ABC; B...

Question

In $Δ A B C; B M ⊥ A C$ and $C N ⊥ A B$ ,
Hence,
$\frac{A B}{A C} = \frac{B M}{C N} = \frac{A M}{A N}$
If the above statement is true then mention answer as 1, else mention 0 if false

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Solution

Given: $△ A B C$ , $B M ⊥ A C$ and $C N ⊥ A B$
In $△ A C N$ and $△ A B M$ ,
$∠ C A N = ∠ B A M$ (Common)
$∠ A N C = ∠ A M B$ (Each $90^{\circ}$
$∠ A C N = ∠ A B M$ (Third angle)
Thus, $△ A C N \sim △ A B M$ (AAA rule)
Thus, $\frac{A B}{A C} = \frac{A M}{A N} = \frac{B M}{C N}$ (Corresponding sides)

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In ΔABC;BM⊥AC and CN⊥AB,Hence,ABAC=BMCN=AMANIf the above statement is true then mention answer as 1, else mention 0 if false

Given: △ABC, BM⊥AC and CN⊥ABIn △ACN and △ABM,∠CAN=∠BAM (Common)∠ANC=∠AMB (Each 90∘∠ACN=∠ABM (Third angle)Thus, △ACN∼△ABM (AAA rule)Thus, ABAC=AMAN=BMCN (Corresponding sides)

In $Δ A B C; B M ⊥ A C$ and $C N ⊥ A B$ ,
Hence,
$\frac{A B}{A C} = \frac{B M}{C N} = \frac{A M}{A N}$
If the above statement is true then mention answer as 1, else mention 0 if false