Curated OER
Exploring the Orthocenter of a Triangle
Young mathematicians explore the concept of triangles as they construct altitudes of triangles to find the orthocenter. Learners construct their triangles using Cabri Jr. on their graphing calculators and find that the altitudes of a...
Curated OER
Regents Exam Questions G.G.21: Centroid, Orthocenter, Incenter, and Circumcenter
In this triangles worksheet, learners solve 4 multiple choice problems. Students find the centroid, orthocenter, incenter, and circumcenter or various triangles.
Curated OER
Orthocenter Of a Triangle
Students find the orthocenter of a triangle. In this geometry lesson, students identify where the altitudes meet in a triangle. They use Cabri software to explore acute, obtuse and right triangles.
Curated OER
Properties of the Centers of a Triangle
High schoolers investigate properties of the four centers of a triangle and explore a special property of the circumcenter and orthocenter of a triangle. This instructional activity requires the use of Cabri, Jr.
Curated OER
Concurrence
In this concurrence learning exercise, 10th graders solve 10 different problems related to determining various concurrences. First, they determine which type of triangle has two altitudes outside of it. Then, students determine the...
Curated OER
Medians and Altitudes of Triangles
In this geometry worksheet, 10th graders determine if a given segment is a median or altitude of a triangle and use then find the indicated missing length or equation of a line. The two page worksheet contains twenty...
Curated OER
Altitudes and Orthocenters: Making Connections to the Nine-Point Circle
Students practice various equations for constructing nine-point circles for triangles.
Mathematics Vision Project
Geometric Figures
Logical thinking is at the forefront of this jam-packed lesson, with young mathematicians not only investigating geometric concepts but also how they "know what they know". Through each activity and worksheet, learners wrestle with...
Radford University
Finding a Location for Your Kitchen Island
Where is the best place to work? Small groups map out a kitchen on a coordinate plane and find the centers of the work triangle to find the best place to install an island. The teams use algebraic methods to locate the center by finding...
Illustrative Mathematics
Placing a Fire Hydrant
Triangle centers and the segments that create them easily become an exercise in memorization, without the help of engaging applications like this lesson. Here the class investigates the measure of center that is equidistant to the three...
Curated OER
Lesson 5.3 Vocabulary Quiz: Concurrent Lines, Medians, & Altitudes
In this vocabulary worksheet, students match a given vocabulary word to the correct definition. Words include such terms as altitude, centroid, circumcenter, circumscribed circle, inscribed circle, median and...
Curated OER
Special Segments in a Triangle
In this geometry worksheet, 10th graders review the vocabulary associated with the special segments of a triangle and the associated points of concurrency and solve problems in which they find the indicated missing angle or...
Curated OER
The Search for Pythagoras' Treasure
Students identify and define properties of triangles. In this geometry lesson, students identify the missing sides and angles of right triangles. They use the rules of the Pythagorean Theorem to solve their problems.
Curated OER
Constructing Geometric Shapes
In this construction geometric shapes worksheet, student use the software program for instruction then construction shapes and bisect angles for four questions.
University of Georgia
University of Georgia: Inter Math: Orthocenter
This site from InterMath gives a description of the orthocenter of a triangle along with a visual representation. Be sure to follow the links to related terms, everyday examples, challenging problems, more information, and the...
Texas Instruments
Texas Instruments: Centroid and Orthocenter
In this activity, students analyze the location of the centroid and orthocenter for different triangles.
Texas Instruments
Texas Instruments: The Orthocenter of a Triangle
Students understand that the orthocenter is the point of concurrence of the three altitudes of a triangle. They construct circumcircles and Feuerbach circles and determine the relationship between them.
Math Open Reference
Math Open Reference: Orthocenter of a Triangle
Learn about the orthocenter of a triangle with this handy reference guide. Provides a detailed definition, examples, and an interactive activity that enhances further explanation. Includes links to related topics.
Wolfram Research
Wolfram Math World: Orthocenter
This site from MathWorld provides a diagram of a triangle with its orthocenter labeled. The site details how to find the orthocenter with links to the key terms. The site details many other interesting properties of the triangle...
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Characteristics of an Orthocenter
Here at The Math Forum, Dr. Math offers interesting properties of orthocenters. Links are provided at the bottom of the page for information on associated topics.
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Constructing the Orthocenter
Dr. Math shows how to construct the orthocenter of any triangle using a compass and straight edge.
Cut the Knot
Cut the Knot: Existence of the Orthocenter
This site defines the altitude of a triangle and gives the standard notation for altitudes of a triangle. The site then goes to list several proofs involving altitudes and orthocenters.
University of Georgia
University of Georgia: Altitudes & Orthocenters: Making Connections
This site describes altitudes and orthocenters in triangles and their connections with the nine-point circle.
CK-12 Foundation
Ck 12: Altitudes: Orthocenter
[Free Registration/Login Required] Students will use the interactive riangle and points to explore altitudes such as the orthocenter. Click learn more to watch a video and click challenge me to answer a practice question.