In an isosceles trapezoid, the diagonal is the bisector of the acute angle of the trapezoid.

In an isosceles trapezoid, the diagonal is the bisector of the acute angle of the trapezoid. Knowing that the larger base is 17 and the side is 10, find the perimeter of the trapezoid.

1. A, B, C, D – the tops of the trapezoid. BD is the diagonal. Larger base AD = 17 cm. AB = 10 cm.

2. ∠ADВ = ∠ВDC, since the bisector ВD divides ∠Д into two equal angles.

3. ∠АДВ = ∠СВD as angles at parallel sides ВС and АD and diagonal BD crossing them.

4. Hence, ∠СВD = ∠ВDC. Therefore, the triangle CBD is isosceles. BC = CD.

5. The sides are equal to the isosceles trapezoid, that is, AB = CD = 10 cm.

6. The perimeter of the trapezoid = AB + CD + AD + BC = 10 + 10 + 17 + 10 = 47 cm.