Tangrams are sets of seven geometrical shapes consisting of one square, one parallelogram, two small right isosceles triangles, one medium right isosceles triangle and two large right isosceles triangles. All seven shapes arrange into a square. Math teachers use tangrams to teach geometric principles in an entertaining way. Students often enjoy the challenge of arranging the shapes to create pictures and other geometric shapes. Generally, a puzzle is only considered solved if all seven pieces are used. There are at least two ways to create a trapezoid, a four-sided shape with two parallel sides, using all seven tans, or pieces.
Place one of the large right triangles on the table with the right angle on the bottom right side. Place one of the small triangles next to the large triangle so that the right angle of the small triangle is touching the right angle of the large triangle. The right angles should match and the sides of both triangles should be touching without a gap.
Place the parallelogram next to the small triangle so that the long side of the parallelogram runs along the long side of the small triangle. The bottom edges of the large triangle, small triangle and parallelogram should create a straight line.
Slide the square into place above the parallelogram so it fills the space alongside the vertical edge of the large triangle and above the top horizontal side of the parallelogram.
Place the second small triangle next to the square, arranged so that the right angle of the triangle is touching the upper right angle of the square. The vertical side of the triangle should be flush with the right side of the square.
Place the medium triangle inside of the space left by the parallelogram and the second small triangle. The long side of the medium triangle should be vertical, and the right angle should fit in where the corners of the parallelogram, square and second small triangle meet.
Place the final shape, the second large triangle, to the right of the medium triangle. The right angle of the large triangle should be facing the bottom left, and the vertical side of the large triangle should be flush with the long side of the medium triangle. When the last piece is in place, you will see an isosceles or regular trapezoid with two parallel bases and two sides of the same length.
Place one large triangle on the table so that the long side is vertical and the right angle points to the right like an arrow. Arrange the medium triangle so the long side is flush with the lower diagonal side of the large triangle. The right angle of the medium triangle should be on the bottom right side of the shape.
Orient one small triangle so that its long side is horizontal and the right angle is pointing down like a down arrow. Slide the small triangle into place so its left corner touches the top corner of the large triangle and the short sides align. The small triangle's short side will only cover the top half of the large triangle's short side.
Rotate the square so the corners point up, down, left and right like a diamond. Slide it into the right angle created by the large and small triangles already placed.
Slide the parallelogram into place so that one short side aligns with the side of the square and one long side aligns with the vertical edge of the medium triangle. The sides should be flush and fit perfectly along the edges.
Orient the remaining small triangle so the long side is vertical and the right angle points toward the right. Match up the long side of the small triangle with the right vertical edge of the parallelogram.
Orient the final large triangle so the long side is horizontal and the right angle is pointing up. Slide the large triangle into place so the right diagonal short side lines up along the bottom short side of the parallelogram and the bottom short side of the small triangle. After the final shape is in place, you will see a right trapezoid that has two right angles and two parallel bases.
Rotate and flip each tangram piece as needed to find the proper arrangement.