Question

The line segments joining the midpoints of the sides of a triangle form four triangles, each of which is ______.

Options

• congruent to the original triangle

• similar to the original triangle

• an isosceles triangle

• an equilateral triangle

Answer 1

The line segments joining the midpoints of the sides of a triangle form four triangles, each of which is similar to the original triangle.

Explanation:

Let D, E, F be the midpoints of BC, CA, AB. By the midpoint theorem FE || BC and similarly the other midpoint segments are parallel to the corresponding sides. Hence, corresponding angles of each small triangle and the original triangle are equal (AA), so each small triangle is similar to the original. Each small triangle has linear scale factor `1/2`.