In an isosceles triangle MNK, point D is the midpoint of the base of MK, DA and DB are perpendiculars

| June 22, 2021 | education

In an isosceles triangle MNK, point D is the midpoint of the base of MK, DA and DB are perpendiculars to the lateral sides. Prove that angle ADN = angle BDN.

First, consider the triangle MNK, in which ND is the median of an isosceles triangle, it is also the height and bisector for such a triangle. Hence, the angles are <MND = <DNK.

Consider triangles AND and BND, in this triangle, AND, the angle is <ADN = 180 ° – <DAN – <AND = 180 ° – 90 ° – <AND = 90 ° – <AND.

In triangle BND, the angle under consideration is <NDB = 180 ° – <NBD – <BND = 90 ° – <BND.

We got that <ADN = 90 ° – <AND, and the angle <NDB = 90 ° – <BND. That is, we got that these angles are equal to 90 ° – equal angles (<MND = <DNK), that is, they are also equal to each other, which was required to be proved.



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