Please help Match each numbered statement in the proof with the correct reason.
Options:
Definition of supplementary angles
Supplementary Angles Theorem
Given
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.

We basically re-state what the instructions say just to set up the start of the proof. This is true for any proof you will do.

The definition of supplementary angles is basically if two (or more) angles add to 180, then they are supplementary.

Try not to confuse this with "supplementary angles theorem" which says that if two angles (say x and y) are supplementary to a third angle (say angle z) then x = y. So more formally, if x+z = 180 and y+z = 180, then x = y. This can be proved through a bit of algebra.

This is a very wordy way of saying "consecutive angles of a parallelogram are supplementary". Note how angle S is next to angles R and T.

So because S+R = 180 and S+T = 180, this means we have a parallelogram.

We could prove that angle R is congruent to angle T (supplementary angles theorem) and then show that opposite angles being congruent leads to a parallelogram. So there are often many paths to the same answer. In this particular case however, your teacher wants you to use statement 2 to directly go to statement 3.

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