In the parallelogram of ABCD, the diagonal ac is the bisector of the angle and find the side of the BC if the perimeter of ABCD is 48.
| December 13, 2020 | education
Since AC is the bisector of angle A, angle BAC = angle CAD. Angles CAD and BCA – internal cross, lying parallel to AD and AC – secant. This means that the angle BCA = angle BAC => triangle ABC – isosceles, AB = BC. Parallelogram perimeter = 2 * (AB + BC) = 48 => AB + BC = 24 <=> 2 * BC = 24 <=> BC = 12.
Answer: BC = 12.
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