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Option B: and
, so
is supplementary to both
and
, so EFGH is a parallelogram.
Option C: so EFGH is a parallelogram.
Option D: so EFGH is a parallelogram.
Explanation:
Option A: and
so
is supplementary to both
and
, so EFGH is a parallelogram
Let us substitute and
in
,
and
to determine the exact measures the angles of the parallelogram.
Substituting, we get, ,
Thus, because the measures of these angles are not equal.
Hence, Option A is not the correct answer.
Option B: and
, so
is supplementary to both
and
, so EFGH is a parallelogram.
Let us substitute and
in
,
and
to determine the exact measures the angles of the parallelogram.
Thus, substituting, we have, ,
Hence, Option B is the correct answer.
Option C: so EFGH is a parallelogram.
To determine the angles, let us substitute in
and
Thus,
Since, the opposite angles of a parallelogram are equal, EFGH is a parallelogram.
Hence, Option C is the correct answer.
Option D: so EFGH is a parallelogram.
Let us substitute and
in
,
and
to determine the exact measures the angles of the parallelogram.
Substituting, we have, ,
Adding the angles E and G, we have,
By the property of parallelogram, any two adjacent angles add upto 180.
Thus, the adjacent angles E and G add upto 180.
Hence, Option D is the correct answer.
let's recall that perpendicular lines have negative reciprocal slopes, so say for a line with a slope of a/b
a perpendicular one will be -b/a.
what does that mean? well, that the lines are perpendicular of course, they meet at a 90° angle, and two straight lines meeting at 90° can only meet once.
since a solution to a system of equations is where the graph meet, and these two meet perpendicularly once, then that means only one solution.