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Triangle Teacher Resources
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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.
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.
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.
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.
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.
This is an excellent lesson plan for exploring the criteria for triangle congruence. After a review of the definition of congruent triangles, students 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.
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 students.
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.
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.
Ninth graders investigate the properties of similar triangles. In this similar triangle instructional activity, 9th graders use an extension to the story of Aladdin. Students collaborate and problem-solve using the sun and shadows to determine the height of a tree. Resources are provided.
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.
Not all triangles are alike! Scholars participate in an interactive poster project as they explore how angles and sides differentiate triangles. Hook your class by showing the linked clip (about one minute long) from the film A Walk to Remember which demonstrates some of these concepts. After going over the various types of triangles (consider projecting the attached guide), give scholars some guided practice using the linked online interactive tools. Geometers synthesize this information by creating and presenting an interactive poster; however the tutorial link may not work. Consider using another free poster program like Glogster.com.
Starting simply, scholars begin by tracing two triangles before drawing one or two on their own. Next, they examine three pictures to determine how many triangles they see in each. Learners record their answers, practicing writing single-digit numbers. Once they finish, they could try to create their own triangle picture for others to spot the shapes in.
Math wizards explore the midsegment of a triangle. They construct the midsegments of a triangle and investigate the relationship between the length of the midsegment and the length of the side of the triangle. Ti-nspire handheld and the appropriate application are required.
In 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.
Learners use the inequality theorem to solve triangles and their properties. For 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.