Given points A (1; 5) B (-2; 2) C (0; 0) and D (3; 3) prove that ABCD is a parallelogram
| August 14, 2021 | education
Knowing the coordinates of the vertices of the quadrangle ABCD, we determine the slopes of the straight lines AD and BC, AB and CD.
tgα = (Y2 – Y1) / (X2 – X1).
tgAD = (3 – 5) / (3 – 1) = -2 / 2 = -1.
tgBC = (0 – 2) / (0 – (-2)) = -2 / 2 = -1.
tgAB = (2 – 5) / (-2 – 1) = -3 / -3 = 1.
tgCD = (3 – 0) / (3 – 0) = 3/3 = 1.
Since tgAD = tgBC, then AD is parallel to BC, similarly, AB is parallel to CD, hence ABCD is a parallelogram, which was required to be proved.
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