4.(03.02 MC) Nina has prepared the following two-column proof below. She is given that ZOLN & CLNO and she is trying to prove that OL 2 ON.
Step Statement
Reason
1 ZOLN ELLNO
Given
2 Draw OE as a perpendicular bisector to LNby Construction
3 LLEO NEO
Transitive Property of Equality
mZLEO = 90°
Definition of a Perpendicular Bisector
5 m2NEO = 90°
Definition of a Perpendicular Bisector
6 LE EN
Definition of a Perpendicular Bisector
7 ΔOLER ΔΟΝΕ
Side-Angle-Side (SAS) Postulate
8 OL ON
CPCTC
4
Nina made two errors in the proof. Identify and correct the errors. (10 points)

∠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.

c = 0.429t

step-by-step explanation:

the constant rate at which carlos harvests cassava is 35 minutes per 15 cassavas 15/35 = 0.429 cassava per minute

therefore, an equation that models the number of cassava (c) that harvest carlos in a time (t) is the following:

where t is the time in minutes.

this means that when 35 minutes have elapsed 15 cassava have been harvested, at 70 minutes 30 cassava have been harvested and so on.

the answer is a

step-by-step explanation: