Prove that the quadrangle with vertices A (0.1), B (4,3), C (5,1) D (1, -1) is a rectangle?
| September 9, 2021 | education
Find the angles of a given quadrangle:
AB = ((4 – 0); (3 – 1)) = (4; 2);
AD = ((1 – 0); (-1 – (-1)) = (1; 0);
cos (A) = AB * AD / | AB | * | AD | = (4 * 1 + 2 * 0) / √ (16 + 4) * √ (1 ^ 2 + 0 ^ 2);
A = 90 °.
Similarly, we get B = 90 °, C = 90 °, D = 90 °.
Therefore a 4-gon is a rectangle
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