Question

proofs with parallel lines and transversals
geometry - proofs with parallel lines and transversals
given: lines b and c are parallel
and line a is a transversal.
prove: ∠1 is supplementary to ∠7.

1. the last statement in a proof

is always...
a given statement
something you
noticed in the diagram
what needs to be
proved
never relates to
anything else
previously stated.

Explanation:

In a proof, the goal is to establish a particular statement. The given information and intermediate steps (like using theorems, definitions) are all directed towards showing the final result. The last statement in a proof is what the entire proof was structured to demonstrate, which is “what needs to be proved”. The “given statement” is at the start (steps 1 - 2 in the provided proof example), noticing something in the diagram is part of the reasoning process (but not the end - goal), and proofs are logical progressions where each step relates to previous ones (so the option “never relates to anything else previously stated” is incorrect).

Answer:

What needs to be proved