Question

Place a ruler upright in the shadow of the tree, so that the end of its
shadow is at the same place as the end of the shadow of the tree.
Knowing the relevant distances, the height of the tree can be estimated.
As part of this project students should think of examples involving
different geometrical properties of triangles.

Answer 1

The examples involving different geometrical properties of triangles are as follows:

• Basic proportionality theorem
• If a line is parallel to a side of a triangle which intersects other 2 sides at 2 different points, then the line divides other 2 sides in proportion.
• For example: A triangular-shaped field divided into 2 unequal parts by a single line.  
• Pythagoras theorem
• In a right-angled triangle the square of the longest side of the triangle is equal to the sum of squares of remaining 2 sides.
• For example: An electric pole bent towards the wall of the building.
• Angle bisector property
• In a triangle, the angle bisector divides the side opposite to the angle in the ratio of remaining sides.
• For example: A triangular-shaped paper's area can be found by just finding half the area of the paper.