Achord of a circle is a line segment connecting any point on the circle to the center of the circle. true or false.

False.

Step-by-step explanation:

We have been given a statement and we are asked to determine whether our given statement is true or false.

Statement:

A chord of a circle is a line segment connecting any point on the circle to the center of the circle.

We know that chord of a circle is a line segment, whose both ens points lie on the circle. The line line segment connecting any point on the circle to the center of the circle is known as radius of the circle, therefore, our given statement is false.

.

step-by-step explanation:

∠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.