# Activities to Teach Students to Construct the Circumcenter or Incenter of a Triangle

Teaching geometry can be tough, especially when it comes to theorems that require students to use specific formulas and calculations in order to construct points or lines. Two of these theorems are those related to circumcenter and incenter of a triangle. However, there are a variety of activities that teachers can use to help their students understand how to construct these points.

1. Using technology:

There are a variety of apps and websites available that allow students to draw and construct triangles. This can be a great way to introduce them to the concept of circumcenter and incenter, as they can manipulate the triangle and watch the points move in real-time. Some popular options include GeoGebra, Desmos, and DeltaMath.

2. Hands-on activities:

Many students learn best by doing, so hands-on activities that require them to physically construct the circumcenter or incenter of a triangle can be very effective. Some ideas include using string and pins to create the triangle and then finding the point where the strings intersect to identify the circumcenter or incenter, or using manipulatives like pattern blocks or tangram pieces to create the triangle and then visually identify the points.

3. Collaborative group work:

Students can work in groups to create triangles and then use shared resources like pencils, compasses, and rulers to construct the circumcenter or incenter. This allows students to work together to problem-solve and discuss strategies, which can be particularly helpful for those who struggle with this concept.

4. Real-world applications:

Teachers can relate the concept of circumcenter and incenter to real-world applications like architecture or engineering, where triangles and angles are used to construct buildings or bridges. This can help students see the practical use of these theorems and motivate them to learn how to construct these points.

5. Interactive computer simulations:

Interactive computer simulations can be a great way to reinforce the concepts and provide students with a visual understanding of the construction. One popular option is the “Triangle Explorer” simulation on the PhET website, which allows students to manipulate the vertices of a triangle and watch as the circumcenter and incenter move in response.

Overall, there are many activities teachers can use to help students construct the circumcenter or incenter of a triangle. By using a variety of strategies – from hands-on activities to technology-assisted learning – teachers can engage students and support them as they build a solid foundation in geometry.