The diagonal of an isosceles trapezoid divides its acute angle in half.

The diagonal of an isosceles trapezoid divides its acute angle in half. The perimeter of the trapezoid is 15 m and the larger base is 6 m. Find the smaller base of the trapezoid.

1. By the condition of the problem, an isosceles trapezoid is given.

By definition, such a trapezoid has equal sides.

2. It is known that the perimeter of the trapezoid is 15 centimeters.

Let’s write the expression for the perimeter P.

P = 2 * side + larger base + smaller base.

3. It is given that the diagonal divides the acute angle in half.

This means that the triangle formed by the side, the diagonal and the smaller base is isosceles, because the angle between the diagonal and the larger base is equal to the angle between the diagonal and the smaller base (like criss-crossing angles with parallel bases of the trapezoid) and is equal to the angle between the diagonal and the side according to the problem statement.

4. Found that the side of the trapezoid is equal to its smaller base.

Then P = 3 * smaller base + larger base = 15 cm;

Smaller base = (15 – larger base): 3 = (15 – 6): 3 = 3 cm.

Answer: The smaller base of the trapezoid is 3 centimeters