Question

PLEASE HELP ITS DUE SOON! I DONT GET ANY OF THIS! HELP WOULD BE MUCH APPRECIATED! NEED THIS DONE BEEN STUCK ON THIS FOR WAY TO LONG!

YOU WILL GET 100 POINTS IF YOU HELP! QUESTION DOWN BELOW!!!!!

Answer 1

So, we know BC is parallel to EF and 1 is congruent to 3.

Angles between parallel lines have special relationships. The relationships between 2 and 3 is that they are Same-side Interior Angles. This means that angles on the same line, formed by parallel lines intersecting that line (and the angles are on the same side of their respective line) are congruent. So, 2 and 3 are congruent... But by the transitive property, if 1 = 3 and 3 = 2... 1 = 2! And if 1 = 2, they are also Same-side interior angles and thus, the lines they lie on are parallel! So, since 1 and 2 are congruent, AB is parallel to DE.

Answer 2

See below.

Explanation:

Corresponding Angles Postulate

When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.

`\begin{array}c\sf Statement & \sf Reason\\\cline{1-2} BC \parallel EF & \phantom{\frac11}\sf Given\\\\\angle 2=\angle 3 & \textsf{Corresponding Angles Postulate}\\\\\angle 1=\angle 3 & \sf Given\\\\\angle 1=\angle 2 & \textsf{Transitive property of equality}\\&(\angle 2=\angle 3 \; \textsf{and} \; \angle 1=\angle 3)\\\\AB \parallel DE & \textsf{Corresponding Angles Postulate}\\& \textsf{as} \;\angle 1=\angle 2\end{array}`

As DE intersects the two parallel lines BC and EF, ∠2 is congruent to ∠3 (corresponding angles postulate).

As ∠1 = ∠3 and ∠2 = ∠3, then ∠1 = ∠2 (transitive property of equality).

Therefore, as ∠1 and ∠2 are congruent, AB and DE must be parallel (BC is the transversal).