Question

What is the difference between sketching and constructing geometric figures? Give a real-world example of each.

Answer 1

Constructing is when you are given and line or an angle or something and you need to use your protractor and compass to construct what the instructions say. 

Sketching is just like a quickly drawing something out to help you with the problem. For example it says sketch an 80degree angle so you just sketch it without any tools... 

Drawing is like it says "draw an 80degree angle) and you take your protractor and draw an 80degree angle

Answer 2

Sketching = only a rough ideas how an object should be
Constructing = the actualization of that idea

For example in order to build a tower, architects tend to make prior planning with their sketching.
After the sketching is done, they will start to build the tower based on the sketch that they made. The results may not be 100% similar, but it's good to have a sketch to be held as a guidance on constructing the geometric figures

hope this helps