An isosceles triangle has two sides of equal length. (Inclusive definitions state that isosceles triangles have "at least" two sides of equal length, and allow equilateral triangles to be considered isosceles as well.) Beginning students can use nonstandard measurements to create isosceles triangles; activities can be as simple as creating toothpick triangles with a set of matching sides.
Isosceles triangles have two equal angles (or "at least" two equal angles). Young children can informally gauge the size of angles using nonstandard units such as the point of a pattern block or the corner of a page; they can also fold paper triangles to compare angle size. Older students can learn to use protractors.
Isosceles triangles have a single line of reflectional symmetry. It bisects the noncongruent side at a perpendicular angle. Chilren can fold triangles or use mirrors to mark the line of reflective symmetry.
Young students should have opportunities to create new shapes using congruent isosceles triangles. They will discover a range of composite quadrilateral and irregular figures. They should also practice dividing isosceles triangles. For a challenge, children can create artwork to demonstrate how isosceles shapes relate to other geometric figures.
The term isosceles can also refer to the trapezoid, a quadrilateral with a single pair of parallel sides. Much like the triangle, an isosceles trapezoid has a pair of equal non-parallel lines, a single line of reflective symmetry and a pair of matching angles.
Some students, particularly at a young age, have already formed schema for how triangles should look. Some may have difficulty identifying a triangle on a page if its "point" is not oriented on top. Others may believe an isosceles triangle is always "long and skinny," although the non-congruent side can be either longer or shorter than the congruent sides. Some definitions overlap; for example, some right triangles and all equilateral triangles can also be classified as isosceles. For this reason, students studying isosceles shapes should experiment with a variety of examples and non-examples.