Properties of Triangles - Activity

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

1. Step 1

   1. Cut the shape of any triangle out of a sheet of paper

   2. Ensure that it is a "general" triangle shape like a scalene triangle.

   3. Name the triangle as ABC.

   4. In this triangle BC is the base and A is the vertex.

2. Step 2

   1. Identify the Altitude from A to the base BC.

   2. For convenience it has been shown as a dotted line

   3. Name the Altitude as AD.

3. Step 3

   1. Fold the smaller triangle ACD, vertically along the altitude AD, so that side CD is collinear with side BD

4. Step 4

   1. Open out the fold so that the triangle is back to its original flat shape.

   2. It would have a crease along AD

   3. Fold the triangle along AD such that A coincides with D, forming a trapezium BEFC

   4. Hence the height of the trapezium would be half the height of the triangle.

5. Step 5

   1. Identify the altitudes from E & F to the base BC. They have been shown as dotted lines.

   2. Identify isosceles triangles BED & AFC. Why are they isosceles triangles?

6. Step 6

   1. Fold triangle BED along the altitude EG so that B coincides with A/D

   2. Fold triangle AFC along the altitude FH so that C coincides with A/D

   3. 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.

   1. Hence the sum of A, B & C is a Straight Angle

   2. We started with a “general” scalene triangle

   3. Hence it proves that “the sum of the interior angles of any triangle is a straight angle”

2. Area of a triangle – 1

   1. Triangle ABC folds without any overlap into the rectangle EFGH.

   2. It is obvious that Area of rectangle EFGH is twice the area of triangle ABC.

   3. Length of rectangle EFGH, which is GH, is half the base of the triangle BC.

   4. Height of rectangle EFGH, which is EG or FH, is half the height of the triangle ABC.

   5. Hence the Area of triangle ABC equals

   6. 2 X area of rectangle EFGH, which equals

   7. 2 X length X height of rectangle EFGH, which equals

   8. 2 X ½ the base of the triangle ABC X ½ the height of the triangle ABC

   9. ½ Base X Height of triangle ABC

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