Triangles
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Area of Parallelograms - Activity A
Examine and manipulate the graph of a parallelogram or triangle and find its area. Explore the relationship between the area of … a parallelogram and the area of a rectangle using an animation.
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Area of Parallelograms - Activity B
Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. Also, with the help of … an animation, see that any triangle is half of a parallelogram.
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Bisectors in Triangles
Explore the special properties of a point that lies on the perpendicular bisector of a segment, and of a point that lies on an … angle bisector. Manipulate the point, the segment, and the angle to see that these properties are always true.
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Classifying Triangles
Place constraints on a triangle and determine what classifications must apply to the triangle.
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Concurrent Lines, Medians, and Altitudes
Explore the relationships between perpendicular bisectors, the circumscribed circle, angle bisectors, the inscribed circle, altitudes, … and medians using a triangle that can be resized and reshaped.
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Congruence in Right Triangles
Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions … the triangles are guaranteed to be congruent.
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Isosceles and Equilateral Triangles
Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles.
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Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence.
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Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the … two triangles.
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Triangle Angle Sum - Activity A
Measure the angles of a triangle and find the sum. Then reshape and resize the triangle and confirm that the sum of angle measures is … the same for all triangles.
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Triangle Angle Sum - Activity B
Measure the angles of a triangle and find the sum. Then reshape and resize the triangle and confirm that the sum of angle measures is … the same for all triangles.
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Triangle Inequalities
Discover the inequalities related to the side lengths and angle measures of a triangle. Reshape and resize the triangle to confirm that … these properties are true for all triangles.
