The diagonals AC and BD of the isosceles trapezoid ABCD are the bisectors of the angles

| March 2, 2021 | education

The diagonals AC and BD of the isosceles trapezoid ABCD are the bisectors of the angles at the base of AD. Find the perimeter of the trapezoid if its bases are 6 cm and 10 cm.

Before making a decision, you need to make a drawing.

Consider a triangle ABC: the angle BAC is equal to the angle CD (AC is the bisector), the angle DAC is equal to the angle of BCA (internal criss-crossing angles with parallel BC and AD and secant AC). This means that the angle BAC is equal to the angle of the BCA, and therefore, the triangle ABC is isosceles.

AB = BC = 6 cm.

Similarly, we consider the triangle ACD and prove that it is isosceles.

CD = BC = 6 cm.

Find the perimeter of the trapezoid:

P (ABCD) = AB + BC + CD + AD = 6 + 6 + 6 + 10 = 28 (cm).

Answer: the perimeter of the trapezoid is 28 cm.



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