In the rectangle MРKН, the diagonals intersect at point O. on the side of the MK, the perpendiculars

| September 4, 2021 | education

In the rectangle MРKН, the diagonals intersect at point O. on the side of the MK, the perpendiculars RA and HB are drawn. it is known that MA = OB. find the corner of the РOM.

Let us prove that the triangle OAP is equal to the triangle OВН. Both triangles are rectangular, since AP and BN are perpendicular to MK, OP = OH, since the diagonals at the point of their intersection are halved, the angle AOP = ВOН as vertical, then the triangles are equal in hypotenuse and acute angle.

Then OB = OA, and since MA = OB, then MA = OA, which means that AB is not only the height of the OРM triangle, but also the median, then in the OРM triangle MR = OP. And since OP = OM as half of the diagonals, the triangle OPM is equilateral and its internal angles are 60.

Answer: The POM angle is 60.



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