In an isosceles trapezoid, the diagonal is the bisector of an acute angle, one of the bases is greater

| May 31, 2021 | education

In an isosceles trapezoid, the diagonal is the bisector of an acute angle, one of the bases is greater than the second. Find the middle line of a trapezoid if its perimeter = 74cm.

By the condition AC is the bisector of the angle BAD, then the angle BAC = DAC.

Angle BAC = DAC as criss-crossing angles at the intersection of parallel straight lines BC and AD secant AC.

Then the angle BCA = BAC, and therefore the triangle ABC is isosceles, AB = BC, and since the trapezoid is isosceles, then AB = BC = CD.

Let AB = BC = CD = X cm, then AD = (X + 6) cm.

The perimeter of the trapezoid is: Ravsd = (AB + BC + CD + AD) = 74 cm.

(X + X + X + X + 6) = 74 cm.

4 * X = 74 – 6 = 68 cm.

= 68/4 = 17 cm.

BC = 17 cm.

AD = 17 + 6 = 23 cm.

Determine the length of the midline of the trapezoid.

KM = (BC + AD) / 2 = (17 + 23) / 2 = 20 cm.

Answer: The length of the middle line of the trapezoid is 20 cm.



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