In an isosceles trapezoid, the diagonals are the bisectors of its obtuse angles.

In an isosceles trapezoid, the diagonals are the bisectors of its obtuse angles. find the perimeter of the trapezoid if the lengths of the bases are 5 cm and 8 cm.

1. A, B, C, D – the tops of the trapezoid. AC and BD are diagonals. Smaller base BC = 5 cm. Larger base AD = 8 cm.

2. ∠АСВ = ∠АСD, since the bisector AC divides ∠С into two equal angles.

3. ∠ACB = ∠САD, as angles at parallel straight lines (bases of the trapezoid) BC and AD and the diagonal AC intersecting them.

Therefore, ∠САD = ∠АСD. The ACD triangle is isosceles. CD = AD = 8 cm.

4. The total length of the sides and bases of the trapezoid (perimeter) is equal to AB + CD + BC + AD = 8 + 8 + 5 + 8 = 29 cm.