In an isosceles trapezoid, the bases are 6cm and 10cm, and the angle at the base is 45 degrees

In an isosceles trapezoid, the bases are 6cm and 10cm, and the angle at the base is 45 degrees. What is the height drawn to the base.

1. A, B, C, D – the tops of the trapezoid. BC = 6 centimeters. BP = 10 centimeters. ВН – height to the base АD. ∠А = 45 °.

2. Based on the fact that the total value of the angles of the triangle AВН is 180 °, we calculate the value of ∠ABН:

∠АВН = 180 ° – 90 ° – 45 ° = 45 °. The indicated triangle is isosceles, since the angles at the side AB are equal.

Therefore, ВН = AН.

3. According to the properties of an isosceles trapezoid, the segment AH = (AD – BC) / 2 = (10 – 6): 2 = 2 centimeters.

4. The height of the HВ is 2 centimeters.