This series of geometric material is used for other purposes, but they are of minor importance.
Fourth Series of Insets: Division of a Triangle. This material made up of four frames of equal size, each containing an equilateral triangle measuring ten centimeters to a side. The different pieces should fill the triangular spaces exactly.
One is filled by an entire equilateral triangle.
One is filled by two rectangular scalene triangles, each equal to half of the original equilateral triangle, which is bisected by dropping a line perpendicularly to the base.
The third is filled by three obtuse isosceles triangles, formed by lines bisecting the three angles of the original triangle.
The fourth is divided into four equilateral triangles which are similar in shape to the original triangle.
With these triangles a child can make a more exact analytical study than he made when he was observing the triangles of the plane insets used in the "Children's House." He measures the degrees of the angles and learns to distinguish a right angle (90°) from an acute angle (<90°) and from an obtuse angle (>90°).
Furthermore he finds in measuring the angles of any triangle that their sum is always equal to 180° or to two right angles.
He can observe that in equilateral triangles all the angles are equal (60°); that in the isosceles triangle the two angles at the opposite ends of the unequal side are equal; while in the scalene triangle no two angles are alike. In the right-angled triangle the sum of the two acute angles is equal to a right angle. A general definition is that those triangles are similar in which the corresponding angles are equal.