The segments AB and DC lie on parallel lines, and the segments AC and BD meet at point M.

| January 9, 2021 | education

The segments AB and DC lie on parallel lines, and the segments AC and BD meet at point M. Find MC if AB = 16, DC = 24, AC = 25.

AB || DC, it means <B = <D (internal criss-crossing with parallel AB and DC and secant BD), <AMB = <DMC (vertical), it means triangles AMB and CMD are similar in two corners. If these triangles are similar, then the corresponding sides of these triangles are proportional.
Let’s denote the segment MC by x, then the segment AM = 25 – x (because the entire length of the segment AC = 25.
AB / DC = AM / MC;
16/24 = (25 – x) / x – the product of the extreme terms of the proportion is equal to the product of the middle terms of the proportion;
16x = 24 (25 – x);
16x = 600 – 24x;
16x + 24x = 600;
40x = 600;
x = 600: 40;
x = 15.
Answer. MS = 15.



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