In the given trapezium the diagonal BD, bisects diagonal AC in the rat

1.	In the given trapezium the diagonal BD, bisects diagonal AC in the ratio 2:1, thenAB is equal to..A)2 AB B) 2 BC C) 2 CD D) 2 BD
Answer» $\huge\boxed{\underline{\mathcal{\red{A}\green{N}\pink{S}\orange{W}\blue{E}\pink{R}}}}$ $\huge\underline\mathcal\green{C) 2CD}$ $\huge{\fbox{\fbox{\orange{\mathfrak{Explanation}}}}}$ $\text{[math]}$ Given, that the diagonal BD divides the AC in AO : OC with 2 : 1 To prove : AB = 2CD Proof : In Δ AOC and Δ DOC AOB = COD OBA = ODC (Because DC is PARALLEL to AB, and DB is transversal. So, these are alternates) THEREFORE, Δ AOB is same as Δ COD (By AA similarity) Now, AO/OC = AB/DC (Because in similar triangles sides are proportional) ➡️ 2/1 = AB/DC (Given that AO : OC = 2 : 1) So, AB = 2CD Hence proved.

In the given trapezium the diagonal BD, bisects diagonal AC in the ratio 2:1, thenAB is equal to..A)2 AB B) 2 BC C) 2 CD D) 2 BD

Answer»

$\huge\boxed{\underline{\mathcal{\red{A}\green{N}\pink{S}\orange{W}\blue{E}\pink{R}}}}$

$\huge\underline\mathcal\green{C) 2CD}$

$\huge{\fbox{\fbox{\orange{\mathfrak{Explanation}}}}}$

$\text{[math]}$

Given, that the diagonal BD

divides the AC in AO : OC

with 2 : 1

To prove : AB = 2CD

Proof : In

Δ AOC and Δ DOC

AOB = COD

OBA = ODC (Because DC is

PARALLEL to AB, and DB is

transversal. So, these are

alternates)

THEREFORE,

Δ AOB is same as Δ COD

(By AA similarity)

Now, AO/OC = AB/DC

(Because in similar triangles

sides are proportional)

➡️ 2/1 = AB/DC

(Given that AO : OC = 2 : 1)

So, AB = 2CD

Hence proved.

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In the given trapezium the diagonal BD, bisects diagonal AC in the ratio 2:1, thenAB is equal to..A)2 AB B) 2 BC C) 2 CD D) 2 BD​

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In the given trapezium the diagonal BD, bisects diagonal AC in the ratio 2:1, thenAB is equal to..A)2 AB B) 2 BC C) 2 CD D) 2 BD