Question

Cut out a triangular piece of card-board. Place a lit up candle or a small lamp on a table. Hold the triangle between a wall and the candle/lamp. Observe the shadow of the triangle. Decide if the triangle and its shadow are similar. (What care will you take so that the triangle and its shadow are similar?)

Answer 1

Hint: In this question, we have a triangular piece of card-board.
By placing the small lamp on a table and holding the triangle between a wall and the candle/lamp the shadow we will get is similar to the original triangle. We need to find out the condition which will make them similar.

Complete step-by-step solution:
We have a triangular piece of card-board, placing a lit up candle or a small lamp on a table and holding the triangle between a wall and the candle/lamp.
We need to find out the condition which will make the shadow of the triangle and the original triangle similar.

If two triangles are similar triangles, it means that one shape can become another using turns , flips and/or slides .
Rotation:

Reflection:

Translation:

When two triangles are congruent they will have exactly the same three sides and exactly the same three angles. Also Two triangles are similar if the only difference is size (and possibly the need to turn or flip one around).

Hence, if the triangle is aligned the triangles are similar but if they are not aligned the sides of the triangles will not be parallel, thus not similar.

Note: In Euclidean geometry, two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling, possibly with additional translation, rotation and reflection.