Homework 1

Choose one of the following theorems (from High School geometry). Type the statement of the theorem in LaTeX, and make an accompanying picture using the TikZ package. Make sure your triangle is scalene and not right so that the picture shows the general case. Provide labels, including those for vertices of triangles and the point of concurrency. Also, depending on the theorem, you will need to label: congruent segments (for medians and side bisectors), perpendicular lines (for altitudes and side bisectors), or congruent angles (for angle bisectors). Your paper should have a title (Homework 1) 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.

• 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.)