# High School: Geometry

### Congruence HSG-CO.D.13

13. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Pop culture is full of daddy issues. In 1974, Harry Chapin's hit Cat's in the Cradle made the world cry and vow to hug and kiss their babies a little more often. The characters on Lost were riddled with them. And we certainly wonder how things would have been different for Luke if only his papa had been around.

What do fathers have to do with the construction of triangles, squares, and hexagons? Well, frankly, nothing. Except that some dads like to help their kids with math homework.

This standard is as basic as they come. Students are expected to construct equilateral triangles, squares, and circle-inscribed regular hexagons. This means they need to know the theorems and rules about these shapes, specifically that each shape is composed of congruent sides and congruent angles.

Students also need to know how to construct congruent line segments and congruent angles. They'll need to be able to draw perpendicular lines, too.

It will be beneficial for students to see demonstrations of how to construct each shape, particularly noting that the side length of the hexagon-in-a-circle is equal to the radius of the circle. (That might be a fun in-class exploration, actually. Can they discover that relationship on their own?)

Once they've finished their homework, we hope these kids can go play a game of catch with their dads.