# In an isosceles trapezoid, the bisector drawn from the apex of an obtuse angle is parallel to the lateral side

In an isosceles trapezoid, the bisector drawn from the apex of an obtuse angle is parallel to the lateral side, calculate the perimeter of the trapezoid if the length of its lateral side is 14 cm, and the smaller base is 17 cm.

The quadrangle ABCK is a parallelogram, since its opposite sides are pairwise parallel, then CK = AB = 14 cm, AK = BC = 17 cm.

In a parallelogram, opposite angles are equal, then the angle ABK = ВСK. Since the CК is the bisector of the angle ВСD, then the angle DCК = ВСК = BAD. Angle CKD = BAD as the corresponding angles at the intersection of parallel straight lines AB and CK secant AD. Angle CDK = BAD as angles at the base of an isosceles trapezoid.

Then in the triangle CDK all angles are equal, which means that the triangle is equilateral, СK = CD = DK = 14 cm.

Base length AD = AK + DK = 17 + 14 = 31 cm.

The perimeter of the trapezoid is: Ravsd = (AB + BC + CD + AD) = (14 + 17 + 14 + 31) = 76 cm.

Answer: The perimeter of the trapezoid is 76 cm.

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