Plan A: Show that opposite sides of the quadrilateral are congruent.
Plan B: Show that the diagonals of the quadrilateral bisect each other.
Use the following information and diagram to answer the question.
Given: Quadrilateral ABDC has vertices at A(2,6), B(6,8), C(1,2), and D(5,4).
Prove: Quadrilateral ABDC is a parallelogram.
Which plan for a proof for this problem will show that quadrilateral ABDC is a parallelogram?
Responses
4 answers
Use the following information and diagram to answer the question.
Given: Quadrilateral ABDC has vertices at A(2,6), B(6,8), C(1,2), and D(5,4).
Prove: Quadrilateral ABDC is a parallelogram.
Which plan for a proof for this problem will show that quadrilateral ABDC is a parallelogram?
A. Use the midpoint formula to find the midpoint of AD¯¯¯¯¯¯¯¯ and BC¯¯¯¯¯¯¯¯. Show that the midpoint for both segments is the same. Since the diagonals of a quadrilateral intersect each other, then the quadrilateral is a parallelogram.
B.Use the midpoint formula to find the midpoint of AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯. Show that the midpoint of these two sides has the same x-coordinate. Then, show that the midpoint of BD¯¯¯¯¯¯¯¯ and AC¯¯¯¯¯¯¯¯ has the same y-coordinate. Thus, the quadrilateral is a parallelogram.
C.Use the midpoint formula to find the midpoint of AD¯¯¯¯¯¯¯¯ and BC¯¯¯¯¯¯¯¯. Show that the midpoint for both segments is the same. By the definition of midpoint and bisect, AD¯¯¯¯¯¯¯¯ and BC¯¯¯¯¯¯¯¯ bisect each other. Since the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
D.Use the midpoint formula to find the midpoint of AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯. Show that the midpoint for both segments is the same. Since opposite sides of a quadrilateral have the same midpoint, then the quadrilateral is a parallelogram.
Given: Quadrilateral ABDC has vertices at A(2,6), B(6,8), C(1,2), and D(5,4).
Prove: Quadrilateral ABDC is a parallelogram.
Which plan for a proof for this problem will show that quadrilateral ABDC is a parallelogram?
A. Use the midpoint formula to find the midpoint of AD¯¯¯¯¯¯¯¯ and BC¯¯¯¯¯¯¯¯. Show that the midpoint for both segments is the same. Since the diagonals of a quadrilateral intersect each other, then the quadrilateral is a parallelogram.
B.Use the midpoint formula to find the midpoint of AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯. Show that the midpoint of these two sides has the same x-coordinate. Then, show that the midpoint of BD¯¯¯¯¯¯¯¯ and AC¯¯¯¯¯¯¯¯ has the same y-coordinate. Thus, the quadrilateral is a parallelogram.
C.Use the midpoint formula to find the midpoint of AD¯¯¯¯¯¯¯¯ and BC¯¯¯¯¯¯¯¯. Show that the midpoint for both segments is the same. By the definition of midpoint and bisect, AD¯¯¯¯¯¯¯¯ and BC¯¯¯¯¯¯¯¯ bisect each other. Since the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
D.Use the midpoint formula to find the midpoint of AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯. Show that the midpoint for both segments is the same. Since opposite sides of a quadrilateral have the same midpoint, then the quadrilateral is a parallelogram.
Why not just show that opposite sides are parallel, that is, they have
the same slope ? That would be so easy to do.
After all, wouldn't it make sense to use the definition of "parallelogram" ?
the same slope ? That would be so easy to do.
After all, wouldn't it make sense to use the definition of "parallelogram" ?
Yes, so the answerer is
Use the midpoint formula to find the midpoint of AD¯¯¯¯¯¯¯¯ and BC¯¯¯¯¯¯¯¯. Show that the midpoint for both segments is the same. By the definition of midpoint and bisect, AD¯¯¯¯¯¯¯¯ and BC¯¯¯¯¯¯¯¯ bisect each other. Since the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Use the midpoint formula to find the midpoint of AD¯¯¯¯¯¯¯¯ and BC¯¯¯¯¯¯¯¯. Show that the midpoint for both segments is the same. By the definition of midpoint and bisect, AD¯¯¯¯¯¯¯¯ and BC¯¯¯¯¯¯¯¯ bisect each other. Since the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.