In a right-angled triangle ABC AC = BC = 32 cm. Find the midline A1B1 of triangle ABC.

A rectangular triangle is a triangle in which one of the corners is a straight line (equal to 90º).

The middle line of a triangle is a line segment that connects the midpoints of its two sides. The middle line of the triangle is parallel to the third side, and its length is half the length of this side:

A1B1 = AB / 2.

To do this, you need to calculate the length of the hypotenuse AB. We apply the Pythagorean theorem, according to which the square of the hypotenuse is equal to the sum of the squares of the legs:

AB ^ 2 = BC ^ 2 + AC ^ 2;

AB ^ 2 = 32 ^ 2 + 32 ^ 2 = 1024 + 1024 = 2048;

AB = √2048 ≈ 45.2 cm;

A1B1 = 45.2 / 2 = 22.6 cm.

Answer: The middle line of the trapezoid is 22.6 cm.