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!

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Answer 1

See below.

Explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Alternate Interior Angles Theorem

If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.

Transitive Property of Equality

If a=b and c=b, then a=c.

Proof that ∠1=∠2

• ∠3 is equal to ∠4 (Vertical Angle Theorem).
• As BC intersects the set of parallel lines AB and CD (given), ∠3 is equal to ∠2 (Alternate Interior Angles Theorem).
• If ∠3=∠4 and ∠3=∠2 then ∠2=∠4 (Transitive Property of Equality).
• Given that ∠1=∠4 and ∠2=∠4 then ∠1=∠2 (Transitive Property of Equality).

`\begin{array}c\sf Statement & \sf Reason\\\cline{1-2}\\ \angle 3 = \angle 4 & \textsf{Vertical Angle Theorem}\\\\AB \parallel CD & \textsf{Given}\\\\\angle 3 = \angle 2 & \textsf{Alternate Interior Angles Theorem}\\\\\angle 2 = \angle 4 & \textsf{Transitive Property of Equality}\\\\\angle 1 = \angle 4 & \textsf{Given}\\\\\angle 1 = \angle 2 & \textsf{Transitive Property of Equality}\\\\\end{array}`