In an isosceles trapezoid, the diagonal is the bisector of an acute angle and divides the midline into 6 cm

univerkov | April 28, 2021 | education

In an isosceles trapezoid, the diagonal is the bisector of an acute angle and divides the midline into 6 cm and 8 cm segments. Find the perimeter of the trapezoid.

1. A, B, C, D – the tops of the trapezoid. ВD = 15 cm. КН – middle line. О – the point of intersection of ВD and КН. EO = 8 cm. HO = 6 cm.

2.KH = EO + HO = 8 + 6 = 14 cm.

3. ∠ADВ = ∠СDВ, since ВD is a bisector.

4. ∠ADВ = ∠DОН as angles at parallel lines AB and KH and the diagonal BD intersecting them.

5. Therefore, ∠НDО = ∠DОН. The DOH triangle is isosceles. OH = DH = 6 cm.

6.CD = AB = 6 x 2 = 12 cm.

7. (BC + AD) ^ 2 = KH.

BC + AD = 2 x 14 = 28 cm.

8. The perimeter of the trapezoid = BC + AD + CD + AB = 28 + 12 + 12 = 52 cm.

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