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Activities on the Isosceles Triangle Theorem

An isosceles triangle is a three-sided geometrical shape in which at least two of the sides are equal. Equilateral triangles, in which all three sides are equal, are a type of isosceles triangle. The isosceles triangle theorem states that the angles opposite to the two equal sides of the triangle are also equal. Like any branch of mathematics, geometry is somewhat abstract, which can make understanding the theorems within it confusing. Implement activities in your classroom to help your students get hands-on experience with this theorem.
  1. Drawing

    • Geometry is a highly visual branch of mathematics. Drawing might seem like a task that belongs in lower grade levels, but asking students to draw a isosceles triangle as you explain the theorem to them can greatly enhance their understanding of the topic. Make sure students are equipped with a ruler to ensure that the two sides of their triangle are equal. Remind students that their drawings are not exactly to scale, so ask them to calculate angles according to the isosceles triangle theorem rather than actually measuring the angles on their drawings.

    Comparisons

    • This activity goes through different geometrical shapes and theorems, highlighting similarities and differences. Geometry is full of theorems and rules, which can be confusing to even the most astute student. If you think your students feel overwhelmed by the information in your geometry section of class, review each shape and theorem. You can do this as a class or hand out a worksheet for students to complete in groups or individually. By the end of the activity, your students should have a much stronger grasp of how the isosceles triangle theorem measures up to the rest of the geometry they've learned so far.

    Worksheets

    • One common activity that helps students practice what they've learned is the worksheet. Before class, make up a list of sample problems. Perhaps the best kind of sample problem to include on a worksheet is one that lists a known angle or side length and asks the student to find a missing angle or side length. For geometry problems like this, you should always include a diagram of the triangle and indicate the two or three equal side lengths. The number and difficulty of sample problems you include is up to you, but it should be based on the previous knowledge and grade level of your class.

    Proofs

    • Proofs are a great classroom activity. Demonstrating the mathematical proof behind a theorem is one way to solidify the information for students, particularly if they are curious about how and why the isosceles triangle theorem works. You can go through the proof as a class, asking for student input at each step, or give students the necessary information to complete the proof and have them work through it in groups or individually. Be sure that your students fully understand the reasoning behind the theorem by the end of the activity.

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