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

 Page 1


CONSTRUCTION
Page 2


CONSTRUCTION
INTRODUCTION
Constructions: The drawing of various shapes using 
only a pair of compasses and straightedge or ruler. No 
measurement of lengths or angles is allowed.
The word construction in geometry has a very specific 
meaning: the drawing of geometric items such as lines 
and circles using only compasses and straightedge or 
ruler. Very importantly, you are not allowed to measure 
angles with a protractor, or measure lengths with a 
ruler.
Page 3


CONSTRUCTION
INTRODUCTION
Constructions: The drawing of various shapes using 
only a pair of compasses and straightedge or ruler. No 
measurement of lengths or angles is allowed.
The word construction in geometry has a very specific 
meaning: the drawing of geometric items such as lines 
and circles using only compasses and straightedge or 
ruler. Very importantly, you are not allowed to measure 
angles with a protractor, or measure lengths with a 
ruler.
BASIC CONSTRUCTION
• 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.
Page 4


CONSTRUCTION
INTRODUCTION
Constructions: The drawing of various shapes using 
only a pair of compasses and straightedge or ruler. No 
measurement of lengths or angles is allowed.
The word construction in geometry has a very specific 
meaning: the drawing of geometric items such as lines 
and circles using only compasses and straightedge or 
ruler. Very importantly, you are not allowed to measure 
angles with a protractor, or measure lengths with a 
ruler.
BASIC CONSTRUCTION
• 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.
1) To Construct the bisector of a given 
angle
Consider ?DEF to construct the bisector.
Steps of construction:
Step 1: With E as centre and small radius draw arcs 
on the rays ED and EF .
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 intersecting point be I.
Step 4: Draw a ray with E as the starting point
passing through I.
EI is the bisector of the ?DEF .
Page 5


CONSTRUCTION
INTRODUCTION
Constructions: The drawing of various shapes using 
only a pair of compasses and straightedge or ruler. No 
measurement of lengths or angles is allowed.
The word construction in geometry has a very specific 
meaning: the drawing of geometric items such as lines 
and circles using only compasses and straightedge or 
ruler. Very importantly, you are not allowed to measure 
angles with a protractor, or measure lengths with a 
ruler.
BASIC CONSTRUCTION
• 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.
1) To Construct the bisector of a given 
angle
Consider ?DEF to construct the bisector.
Steps of construction:
Step 1: With E as centre and small radius draw arcs 
on the rays ED and EF .
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 intersecting point be I.
Step 4: Draw a ray with E as the starting point
passing through I.
EI is the bisector of the ?DEF .
2) To construct the perpendicular bisector of a 
given line segment.
Consider the line segment PQ to construct the
perpendicular bisector.
Steps of Construction:
Step 1: Draw a line segment PQ.
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.