How to find the perimeter of an isosceles trapezoid if the length of the bases is 10 and 5 cm

| January 16, 2021 | education

How to find the perimeter of an isosceles trapezoid if the length of the bases is 10 and 5 cm and the diagonal divides the obtuse angle in half.

1. Let’s designate the vertices of the trapezoid AВСD.
2. Since, according to the problem statement, the ВD diagonal divides the angle at the vertex B in half, the СВD angle is equal to the AВD angle.
3. The angles СВD and ADВ are equal, since they are internal crosswise lying with parallel straight lines BC and AD and secant ВD. Therefore, the AED angle = ADВ angle.
4. The AВD triangle is isosceles, since the angles at the base of the ВD are equal. Sides AB = AD = 10 cm.
5. The perimeter of the trapezoid is: AB + СD + BC + AD = 10 +10 + 5 +10 = 35 cm.
Answer: the perimeter of the trapezoid is 35 cm.



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