Geometrical instruments are used in drawing geometric figures such as triangles, circles, quadrilaterals, polygons etc. with given measuremets. A geometrical construction is the method of drawing a geometrical figure using an ungraduated ruler and a compass.
An angle bisector is a ray, which divides an angle in to two equal parts. The bisector of a line segment is a line that cuts the line segment into two equal halves. A perpendicular bisector is a line, which divides a given line segment into two equal halves and is also perpendicular to the line segment.
Construction of the bisector of a given angle:
Consider ∠DEF to construct the bisector.
Steps of construction:
Step 2: Let the arcs intersect the rays ED and EF at G and H respectively.
Step 3: With centres G and H, draw two more arcs with the same radius such that they intersect at a point. Let the point of intersection be I.
Step 4: Draw a ray with E as the starting point and passing through I.
EI is the bisector of the ∠DEF.
Construction of the perpendicular bisector of a line segment:
Consider the line segment PQ to construct the perpendicular bisector.
Steps of Construction:
Step 2: With P as centre, draw two arcs on either sides of PQ with radius more the half the length of the given line segment.
Step 3: Similarly draw two more arcs with same radius from point Q such that they intersect the previous arcs at R and S respectively.
Step 4: Join the points R and S.
RS is the required perpendicular bisector of the given line segment PQ.
Construction of an angle of 60° at the initial point of a given ray.
Consider ray PQ with P as the initial point. Construction of a ray PR such that it makes angle of 60° with PQ.
Steps of Construction:
Step 2: With P as centre, draw an arc with small radius such that it intersects the ray PQ at C.
Step 3: With C as centre and same radius draw another arc to intersect the previous arc at D.
Step 4: Draw a ray PR from point P through D.
Hence, ∠RPQ is equal to 60°.
Summary
Geometrical instruments are used in drawing geometric figures such as triangles, circles, quadrilaterals, polygons etc. with given measuremets. A geometrical construction is the method of drawing a geometrical figure using an ungraduated ruler and a compass.
An angle bisector is a ray, which divides an angle in to two equal parts. The bisector of a line segment is a line that cuts the line segment into two equal halves. A perpendicular bisector is a line, which divides a given line segment into two equal halves and is also perpendicular to the line segment.
Construction of the bisector of a given angle:
Consider ∠DEF to construct the bisector.
Steps of construction:
Step 2: Let the arcs intersect the rays ED and EF at G and H respectively.
Step 3: With centres G and H, draw two more arcs with the same radius such that they intersect at a point. Let the point of intersection be I.
Step 4: Draw a ray with E as the starting point and passing through I.
EI is the bisector of the ∠DEF.
Construction of the perpendicular bisector of a line segment:
Consider the line segment PQ to construct the perpendicular bisector.
Steps of Construction:
Step 2: With P as centre, draw two arcs on either sides of PQ with radius more the half the length of the given line segment.
Step 3: Similarly draw two more arcs with same radius from point Q such that they intersect the previous arcs at R and S respectively.
Step 4: Join the points R and S.
RS is the required perpendicular bisector of the given line segment PQ.
Construction of an angle of 60° at the initial point of a given ray.
Consider ray PQ with P as the initial point. Construction of a ray PR such that it makes angle of 60° with PQ.
Steps of Construction:
Step 2: With P as centre, draw an arc with small radius such that it intersects the ray PQ at C.
Step 3: With C as centre and same radius draw another arc to intersect the previous arc at D.
Step 4: Draw a ray PR from point P through D.
Hence, ∠RPQ is equal to 60°.