Triangle AKM, ∠A = 90 ° bisector MD is drawn, with DA = 16 cm. Find the distance from point D to line KM.

univerkov | September 23, 2021 | education

The desired distance will be equal to the length of the perpendicular drawn from point D to the hypotenuse KM of the triangle AKM, this is the segment DE.

Consider triangles ADM and EDM, which are rectangular, the angles DMA and DME are equal to each other, since the DM is the bisector of the AMK angle, and the hypotenuse of the DM is common for the triangles. Triangle ADM = EDM by hypotenuse and acute angle, by the third sign of equality of right-angled triangles.

Then DА = DE = 16 cm.

Answer: The distance from point D to straight line KM is 16 cm.

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