Homework 1

Choose a theorem from a High School geometry class. Type the statement of the theorem in LaTeX, and make an accompanying picture using the TikZ package. Include some labels. Depending on the theorem, you may choose to label, for example, points, lenghts, and/or angles. Your paper should have a title and include your name. You may either print your paper and bring it to class or send a link to your Overleaf file to your instructor by email. Below are some examples of theorems, feel free to choose any of these or another theorem.

• Medians in a triangle are concurrent (i.e. intersect at a single point). (Note: the intersection point of the medians is called the centroid of the triangle.)
• Altitudes in a triangle are concurrent. (Note: the intersection point of the altitudes is called the orthocenter of the triangle.)
• Angle bisectors in a triangle are concurrent and their intersection point is the center of the incribed circle. (Note: it is called the incenter of the triangle.)
• Side bisectors in a triangle are concurrent and their intersection point is the center of the circumscribed circle. (Note: it is called the circumcenter of the triangle.)