Notes: Construction | Mathematics & Pedagogy Paper 2 for CTET & TET Exams - CTET & State TET PDF Download

Construction in mathematics typically refers to the precise drawing of shapes, angles, and figures using geometric tools. This skill is essential for understanding and solving geometric problems and is a crucial topic for the CTET and other educational exams. Here's a brief overview:

Compass: Used to draw arcs and circles and to mark equal lengths.

Straightedge (Ruler without markings): Used to draw straight lines.

Protractor: Used to measure and draw angles.

Set Squares: Used to draw right angles and specific angle measurements (usually 30°, 45°, 60°).

Basic Geometric Constructions:

Constructing a Line Segment:

To draw a line segment of a given length, use a ruler to mark the endpoints and then connect them with a straightedge.

Bisecting a Line Segment:

Place the compass at one endpoint of the segment, draw arcs above and below the line.

Repeat with the compass at the other endpoint, creating two intersection points.

Draw a line through the intersection points to bisect the original segment.

Constructing Perpendicular Bisectors:

Bisect a given line segment as described above. The line that bisects the segment at 90° is the perpendicular bisector.

Constructing an Angle Bisector:

From the points where the arc intersects the angle, draw two arcs that intersect each other.

Draw a line from the vertex through the intersection of the arcs to bisect the angle.

Constructing Parallel Lines:

Draw a line and a point not on the line.

From the point, draw a line perpendicular to the original line.

From where this line intersects the original line, draw another perpendicular line through the point. This line is parallel to the original line.

Constructing Triangles:

Given three sides (SSS), draw one side, then use a compass to draw arcs from each endpoint with radii equal to the other two sides. The intersection of the arcs determines the third vertex.

Given two sides and an included angle (SAS), draw one side, then use a protractor to draw the given angle, and then draw the second side from the angle.

Constructing Circles:

To draw a circle, place the compass point at the desired center and adjust the compass width to the desired radius, then draw the circle.

Applications of Geometric Constructions:

Problem Solving: Helps solve complex geometric problems through precise drawings.

Design and Engineering: Essential for technical drawing, architecture, and engineering designs.

Understanding Properties: Facilitates a deeper understanding of geometric properties and relationships.