Task# Two Triangles' Area

Illustrative MathematicsVaries

This task requires the student to draw pictures of the two triangles and also make an auxiliary construction in order to calculate the areas (with the aid of the Pythagorean Theorem). Students need to know, or be able to intuitively identify, the fact that the line of symmetry of the isosceles triangle divides the base in half, and meets the base perpendicularly. Since reflective symmetry belongs to the 8th grade standards, it may be reasonable to assume this knowledge, or the teacher may wish to help students with this part of the picture if they are struggling. Once the student has the appropriate pictures with the perpendicular bisectors drawn the rest of the problem is an application of the Pythagorean theorem.