What you’ll learn
Prove quadrilateral properties with coordinates.
Key idea
Equal finite slopes for both opposite pairs establish a parallelogram.
One parallel pair alone is insufficient; verify both opposite pairs.
Worked example
Complete missing statements or reasons in a proof for 'Prove quadrilateral properties with coordinates'.
Consecutive coordinate vertices are A=(-2, 1), B=(1, 1), C=(2, 6), D=(-1, 6). Complete the proof: AB parallel CD because __; BC parallel AD because __; conclude parallelogram.
- AB and CD have slope 0; BC and AD have slope 5.
- Both opposite pairs are parallel, so the nondegenerate quadrilateral is a parallelogram.
Answer: Both opposite slope pairs match — AB and CD have slope 0; BC and AD have slope 5.
Quick Check
Complete missing statements or reasons in a proof for 'Prove quadrilateral properties with coordinates'.
Consecutive coordinate vertices are A=(-2, 1), B=(3, 1), C=(5, 3), D=(0, 3). Complete the proof: AB parallel CD because __; BC parallel AD because __; conclude parallelogram.