When the denominator of \dfrac{2}{\sqrt{3}} 3 2 start fraction, 2, divided by, square root of, 3, end square root, end fraction is rationalized, it becomes \dfrac{2k}{3} 3 2k start fraction, 2, k, divided by, 3, end fraction. find kkk

Step-by-step explanation:

Given:

On rationalizing the denominator of we get .

To find value of .

Solution.

In order to rationalize a radical denominator we will multiply the numerator and denominator with the radical as multiplying same numbers to numerator and denominator does not effect the proportions. This will remove the radical from the denominator.

For the given fraction with radical 3 in denominator, we will rationalize by multiplying numerator and denominator with radical 3.

So, we have

Rationalizing.

⇒

⇒

We get,

On comparing it with the result given which is

we find out that value of

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

the answer for this question is : 360°

step-by-step explanation:

we have been given a triangle   we need to tell which one of these is a triangle below to map onto itself.

360° rotation is the complete rotation which eventually leads to the same figure which is given.

the correct will be, that is 360° that will cause the triangle below to map onto itself.