Triangle Teacher Resources
Find Triangle educational ideas and activities
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Theorems of Triangles
Show your school spirit while proving theorems about triangles! Your student geometers are charged with coming up with a new design for the school pennant, following specific guidelines. Along the way, they need to prove the theorem that base angles of an isosceles triangle are congruent. Not only is this a learning activity, if you allow time to decorate the pennants, you'll end up with great room or hall decorations.
Discovering the Formula for the Area of a Triangle
Most high schoolers are very familiar with the area of the triangle being equal to 1/2 base times the height. Here, they will develop and test their formula for the area of a triangle when given two adjacent sides and the included angle. After they develop their formula, they will use a dynamic geometry software system, such as Geometer's Sketchpad or GeoGebra to test their conjecture.
Verifying Triangles are Congruent
Here the focus is on triangle congruence. Through an activity that requires investigation, questioning, and working together, geometers learn to identify corresponding parts of triangles to determine if the triangles are congruent. Triangles are transformed through reflection, rotation, and translation.
New! The Health Triangle
What else does physical health include besides exercise and nutrition? How can I support my mental health? Does social health just refer to relationships with friends? How are all of these questions vital to the body's overall efficiency and well being? Discover the primary components of each of the three major areas (physical, social, and mental health) of the health triangle, and discuss what factors can affect and risk one's journey toward lifelong wellness.
Unit Squares and Triangles
This is an interesting geometry problem. Given the figure, find the area of a triangle that is created by the intersecting lines. The solution requires one to use what he/she knows about coordinate geometry, as well as triangle and angle congruence, rigid motion, rotation, translation, and the distance formula. Challenge your learners to find the solution two different ways.
Explore, investigate, and finally prove the angles in a triangle have a sum of 180 degrees. Young geometers use the Interior Angles Theorem, and properties and definitions of congruency.
Criteria for Triangle Congruence
This is an excellent lesson plan for exploring the criteria for triangle congruence. After a review of the definition of congruent triangles, learners work in small groups to rotate through six stations. At each station, they are given three measurements and must determine if the measurements will always produce congruent triangles. Geometers use paper and pencils, patty paper, rulers, and protractors to conduct their investigations. They note their findings on a recording sheet and make conjectures about their results. The activity should give learners a good understanding of SSS, SAS, ASA, and AAS, as well as discounting AAA and SSA as criteria for triangle congruence. Depending on the length of class periods, the lesson may require more than one day to complete.
New! Finding the Area of an Equilateral Triangle
The problem seems simple: find the area of the equilateral triangle whose sides are each length 1. In fact, this same problem is solved in 8th grade, addressing a different Common Core standard, using the formula for area of a triangle to solve. Here the objective is to get geometry learners develop an understanding of two new solutions. One using congruent triangles, and the other using trigonometric ratios.
Mathematics Within: Slope and Triangles
Learners discover a method for determining the slope of a line by creating and comparing similar triangles. They fold coordinate grids to make three similar triangles then measure the sides to compare the relationships between the triangles. The slope equation or rise over run is developed from these relationships.
Triangle Congruence (SSS, SAS, ASA, AAS)
A detailed lesson plan that has learners investigating the criteria necessary for triangle congruence. Working in groups, they visit six different stations. At each station they are given three measurements and are asked to determine if the measurements will always produce congruent triangles. After visiting all six stations, students discuss their findings and generalize the results into SSS, SAS, ASA, and AAS.
New! Triangles Embedded in a Square
Looking for a nice activity that will help deepen your geometry learners' understanding of similar triangles? This activity maps a number of triangles embedded in a square on dot graph paper. Young geometers need to find as many different similar triangle pairs as they can find and justify their solutions.
The Wellness Triangle
Health is not simply the absence of disease or a one-dimensional notion, but is really a combination of physical, emotional, and social components. Discover the wellness triangle, which not only includes signs of health and ways to maintain it, but also emphasizes the need to have balance. The questions provided can be responded to individually, in pairs, or in a whole-group discussion.
Lines of Symmetry for Triangles
What can symmetry tell us about triangles? After looking at four examples, learners will come to realize that lines of symmetry are different for equilateral, isosceles, and scalene triangles. Use this guided practice activity as an introduction to classifying triangles based on their side lengths.
Reflections and Isosceles Triangles
Geometers explore symmetries of isosceles triangles by using rigid transformations of the plane. They complete four tasks, including congruence proofs, which illustrate the relationship between congruence and rigid transformations. The activity requires a thorough understanding of the definition of reflection about a line and is better suited for more sophisticated geometry learners.
Developing 30-60-90 Triangle Relationships
This is a good activity for learners to explore the relationship between the legs and the hypotenuse in 30-60-90 triangles. Using isometric dot paper, geometers follow guided instructions that lead them to discover the special relationship. The instructions are simple, straightforward, and easy to follow. An accompanying worksheet that reviews the Pythagorean Theorem serves as a good introduction to the lesson.
Geometers prove that triangle PQR is congruent to triangle ABC by describing any combination of rotations, reflections, and translations that would prove it so. There is only this single task on the handout, but a detailed explanation of two possible solutions is provided to help you make use of this activity, which is intended to help meet the goals of Common Core Mathematics Standards.
The Greedy Triangle-Intro to Geometric Shapes
In this geometry lesson plan, learners read The Greedy Triangle and use geoboards to construct geometric shapes. They identify the number of sides and angles each shape has.
Triangle Inequality Theorem
Students use the inequality theorem to solve triangles and their properties. In this geometry lesson, students are given spaghetti of different lengths and asked to create triangles. They conclude the necessary length needed to make a triangle and relate it to the inequality theorem.
Students explore triangles. In this geometry lesson, students investigate the properties of triangles by participating in various activities. Such activities include eating triangular-shaped snacks, creating a triangular collage and mobile and singing songs.
For this triangles worksheet, 10th graders solve 3 extensive informal geometry problems that involve triangles. First, they sketch a triangle, selecting 3 of the sides and constructing 3 midpoints. Students then draw each of 3 medians by selecting a vertex and midpoint on the opposite side and constructing a line. Finally, they select one of the vertices of the triangle and check that the ratio does not change.