Find the measure of RT. Assume the drawings are not drawn to scale.

4.5 cm

Step-by-step explanation:

Given that segment RS = 2.0 cm, and segment ST = 2.5 cm, since point R, point S, and point T are collinear, therefore, based on segment addition postulate:

RS + ST = RT

2.0 cm + 2.5 cm = RT (Substitution)

4.5 cm = RT

RT = 4.5 cm.

Thus, the measure of segment RT given above is 4.5 cm.

∠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.