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
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.