Geometry is the study of shapes and sizes and relative positions and proportions of objects. Construction of Shapes is a tricky but very important part of Geometry. It is difficult to understand because construction is done step by step. If you miss or do any of the steps wrong, you end up with something vague. In this chapter, we will learn about the constructions of various shapes.
- Basic Constructions
- Constructions Related to Segment and Triangles
- Construction of Triangles
- Construction of Tangent to a Circle
FAQ on Constructions
Question 1: What are constructions in geometry?
Answer: The drawing of several shapes requires merely a pair of compasses and straightedge or ruler. Thus, no measurement of lengths or angles is allowed. In geometry, ‘construction’ has got a very explicit meaning. It is basically the drawing of geometric items like lines and circles with the use of simply compasses and straightedge or ruler.
Question 2: What are tangents?
Answer: A common tangent may be any line, a ray or a segment which can be a tangent to more than one circle at the same time. Further, there can be one to four numbers of common tangents to two circles. The important point over here is that a tangent of a circle does touch the circle but does not enter it. Besides, multiple tangents to the two circles can be an outer tangent or an inner one to each other’s circles.
Question 3: Which is an example of a line segment?
Answer: The sides of a triangle or square are examples of line segments. Moreover, when both of the endpoints of the segment are vertices of a polygon or polyhedron. Thus, the line segment will either be an edge, of a polygon or polyhedron, if it is adjacent vertices or else a diagonal.
Question 4: How do you do constructions in geometry?
Answer: In geometry, construction refers to drawing shapes, angles or lines exactly. These constructions make use of simply compass, straightedge (i.e. ruler) as well as a pencil. Thus, it is the “pure” form of geometric construction which means it does not involve numbers!