Properties of Triangles

This tutorial is designed to improve and deepen students understanding of the characteristics and properties of triangles.

An applet is used to explore the properties of triangles interactively.

Interactive Tutorial

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1 - Press the button above to start the applet.

2 - A triangle with vertices A, B and C and the values of all its sides, angles (in degrees) and area are displayed. You can
DRAG any vertex of the triangle to change its sides and angles.

3 - Add all three angles of the triangle and round your answer to the nearest degree. What is the answer? Do this activity for several angles. Conclusion.

3 - Explore the famous triangle inequality: "the sum of the lengths of two sides is always greater than the length of the third side". This triangle inequality is equivalent to : "The shortest distance between two points is a straight line."

4 - Explore, for different triangles, that the longest side is opposite the largest angle.

5 - Drag the vertices of the triangle so that the triangle obtained is acute ie all its 3 angles are acute.

6 - Drag the vertices of the triangle so that the triangle obtained is acute ie all its 3 angles are acute.

7 - Drag the vertices of the triangle so that the triangle obtained is obtuse ie the triangle has an obtuse angle.

8 - Drag the vertices of the triangle so that the triangle obtained is an isosceles triangle ie 2 sides of the triangle are (approximately) equal. Check that the 2 angles adjacent to the two equal sides are also (approximately) equal.

9 - Drag the vertices of the triangle so that the triangle obtained is an equilateral triangle ie all 3 sides of the triangle are equal. Check that all 3 angles are (approximately) equal to 60 degrees.

10 - Drag the vertices of the triangle so that the triangle obtained is a right triangle ie one of its angles is (approximately) equal to 90 degrees. You may also want to verify Pythagora's theorem for this triangle.

11 - Use different formulas to obtain the area of triangles and check with the displayed value.

12 - You may also check the
sine and cosine laws.

More geometry references


Geometry Tutorials, Problems and Interactive Applets.