Free Printable Medians and Altitudes worksheets

Start by defining them separately. A median connects a vertex to the midpoint of the opposite side—think 'median to the middle'. An altitude is a segment from a vertex that is perpendicular to the opposite side—think 'altitude for height'. Use dynamic geometry software or physical models to show how they change as you manipulate the triangle's vertices, especially in obtuse triangles where altitudes can be outside the triangle.

Students frequently confuse the two definitions, especially in isosceles or equilateral triangles where a median and an altitude can be the same line segment. They also struggle with altitudes in obtuse triangles, often incorrectly drawing them inside the triangle instead of extending the base to meet the perpendicular line from the opposite vertex.

A good progression includes: 1) Identification problems where students label medians and altitudes in various triangles. 2) Construction exercises using a compass and straightedge or on a coordinate plane. 3) Calculation problems that use the properties of centroids (the intersection of medians) or require the Pythagorean theorem to find lengths.

This topic directly supports the high school geometry domain (G-CO), particularly standards related to geometric constructions and proving theorems about triangles. Understanding medians and altitudes is foundational for exploring points of concurrency like the centroid and orthocenter, which aligns with Common Core's emphasis on applying geometric concepts.

For students needing support, use Wayground's 'Read Aloud' feature or provide worksheets with pre-drawn triangles. For enrichment, challenge students to prove the centroid theorem or explore the properties of the Euler line, which connects the orthocenter, centroid, and circumcenter.

You can assign this worksheet in multiple ways to suit your classroom. Host it as a digital quiz on Wayground for automatic grading, or download the printable PDF for students to complete on paper. Every worksheet includes a full answer key for efficient review. For paper submissions, you can use the Wayground for Teachers app to quickly scan and grade student work.