Properties of Triangles - Activity

We will discover two properties of triangles visually through a paper folding activity.


 * 1) Sum of the internal angles of a triangle is a Straight angle (or 180 degrees)
 * 2) The area of a triangle is 1/2 Base X Height

Please see the above visuals and follow the below-given instructions


 * 1) Step 1
 * 2) Cut the shape of any triangle out of a sheet of paper
 * 3) Ensure that it is a "general" triangle shape like a scalene triangle.
 * 4) Name the triangle as ABC.
 * 5) In this triangle BC is the base and A is the vertex.
 * 6) Step 2
 * 7) Identify the Altitude from A to the base BC.
 * 8) For convenience it has been shown as a dotted line
 * 9) Name the Altitude as AD.
 * 10) Step 3
 * 11) Fold the smaller triangle ACD, vertically along the altitude AD, so that side CD is collinear with side BD
 * 12) Step 4
 * 13) Open out the fold so that the triangle is back to its original flat shape.
 * 14) It would have a crease along AD
 * 15) Fold the triangle along AD such that A coincides with D, forming a trapezium BEFC
 * 16) Hence the height of the trapezium would be half the height of the triangle.
 * 17) Step 5
 * 18) Identify the altitudes from E & F to the base BC. They have been shown as dotted lines.
 * 19) Identify isosceles triangles BED & AFC. Why are they isosceles triangles?
 * 20) Step 6
 * 21) Fold triangle BED along the altitude EG so that B coincides with A/D
 * 22) Fold triangle AFC along the altitude FH so that C coincides with A/D
 * 23) Hence points A, B, C & D meet at a point on the base BC.

From the above activity we can identify the following properties


 * 1) 3 angles A, B & C meet at D without any overlap.
 * 2) Hence the sum of A, B & C is a Straight Angle
 * 3) We started with a “general” scalene triangle
 * 4) Hence it proves that “the sum of the interior angles of any triangle is a straight angle”
 * 5) Area of a triangle – 1
 * 6) Triangle ABC folds without any overlap into the rectangle EFGH.
 * 7) It is obvious that Area of rectangle EFGH is twice the area of triangle ABC.
 * 8) Length of rectangle EFGH, which is GH, is half the base of the triangle BC.
 * 9) Height of rectangle EFGH, which is EG or FH, is half the height of the triangle ABC.
 * 10) Hence the Area of triangle ABC equals
 * 11) 2 X area of rectangle EFGH, which equals
 * 12) 2 X length X height of rectangle EFGH, which equals
 * 13) 2 X ½ the base of the triangle ABC X ½ the height of the triangle ABC
 * 14) ½ Base X Height of triangle ABC

Hence we have proved two important properties of a triangle visually through a paper-folding activity.