Point M does not lie in the plane of the rectangle ABCD of point P and K are the midpoints of the segments
| August 29, 2021 | education
Point M does not lie in the plane of the rectangle ABCD of point P and K are the midpoints of the segments MA and MB. If the CD is 20 cm, then the PK segment is equal to?
From the condition we obtain that ABM is a triangle.
Since the segment РK connects the midpoints of the sides of the triangle, this means that РK is the middle line of triangle ABM.
By the properties of the middle line, we know that the middle line connecting the midpoints of the two sides of the triangle is parallel to its third side and is equal to its half.
Thus, we get that РK = AB / 2.
Since ABCD is a rectangle, its side CD is equal to the side AB as not adjacent. Hence, AB = CD = 20 cm.
RK = AB / 2 = 20/2 = 10.
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