In a rectangular trapezoid MNKP, the angle NMP is straight, the angle NKM is 45 degrees, the angle NKP

| April 2, 2021 | education

In a rectangular trapezoid MNKP, the angle NMP is straight, the angle NKM is 45 degrees, the angle NKP is 135 degrees, the side of MP is 20 cm. 1) find the smaller side of the trapezoid 2) name 3 equal triangles.

Determine the size of the MKR angle. Angle MKR = NKR – NKM = 135 – 45 = 90. Triangle MKR is rectangular.

Triangle MNK is rectangular and isosceles, so one of the acute angles is 45, then MN = KN. Angle MKH = NKH – NKM = 90 – 45 = 45, then triangle MKN is rectangular and isosceles, MH = KH. Then the quadrangle МNКH is square. Since the angle MKR = 90, and the angle MKH = 45, then the angle PKH = 90 – 45 = 45, then the triangle KPH is rectangular and isosceles KH = PH. Then КH is the height, bisector and median of the MKR triangle, and then МH = РH = МР / 2 = 20/2 = 10 cm.Since МNКH is a square, then MN = МH = 10 cm.

Triangles MNK, MKH and PKH are equal on three sides.

Answer: The length of the smaller lateral side is 10 cm. Triangles MNK, MKH and PKH are equal.



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