Some famous models and actors are known for having very symmetric faces. Others have pronounced imperfections that make them beautiful. But just how symmetric is symmetric? Can we use mathematics to compare the symmetry of faces? And how sensitive is our intuition for facial symmetry?

In this lesson, students deepen their understanding of line reflections and line symmetry by drawing on and inspecting a number of famous faces, and develop their own metric for facial symmetry.

### Students will

• Reflect points over the line of symmetry on several faces
• Measure the differences between actual and perfectly symmetrical (reflected) facial features
• Normalize the measures of symmetry to compare photos of different sizes

### Before you begin

Students should be able to explain what it means to reflect a point over a line, and be able to perform a reflection of a point over a line. They should also be able to explain that the line of reflection is the perpendicular bisector of a segment whose endpoints are a point and its reflection (or some version, in their own words, that incorporates those geometric relationships.) This lesson is not meant to serve as students' first encounter with line reflections or dilations, but rather an interesting application. Also, the final question builds on students' previous understanding of scale and similarity.