Download 4 Practical Geometry (Constructions) Objectives: Construct a line

4 Practical Geometry (Constructions)
Objectives:
 Construct a line parallel to a given line
 Construct a triangle given three measurements to identify it uniquely
 Construct a quadrilateral given five measurements to identify it uniquely
Before We Begin:
Terms




Properties
Parallel lines and transversal
Triangles
Congruency
Quadrilaterals


Angle properties of parallel lines and transversal
Congruency criteria for triangles
Lesson Plan: (Chapter 10: NCERT Textbook for Class VII, Chapter 4: NCERT Textbook for Class VIII)
Content
Introduction to Practical
Geometry
Teacher's Activity


Student's Activity
Briefly review the terms and properties

associated with parallel lines, triangles and
congruency by providing clues and inviting
the children to respond with appropriate
terms and properties
Explain how drawing parallel lines,
triangles and quadrilaterals would involve
using these properties to construct scaled
models of the geometrical concepts, using
a protractor, compass and ruler
Revisit the various properties of parallel
lines (transversal and angles), triangles
and congruency
Assignments
Drawing a line parallel to a
given line



Drawing a triangle given
three properties of the
triangle



Through the construction of a line parallel 
to a given line, point out the various
components that go into geometrical
construction:

 Rough diagram
 Understanding the properties
required to construct the figure
 Writing clear and concise steps,
using geometrical language (points,
lines, angles, arcs, intersections,
etc.)
 Constructing the fair diagram using a
well-sharpened pencil
Explain how a parallel line is constructed
using one of the properties of transversal
(e.g. interior alternate angles are equal)
Encourage the students to try constructing
a parallel line using another property (e.g.
corresponding angles are equal)
Understand how a property of parallel
lines, with a transversal, can be used to
construct a line parallel to a given line
Understand the various components of a
geometrical construction and neatly
construct a line parallel to a given line
Review the various congruency criteria for 
triangles: SSS, ASA, SAS and RHS
Point out that if we are to construct a

triangle that exactly matches a given
triangle, then the congruency criteria need
to match. Deduce that the minimum
criteria required to construct a triangle
thus need to match one of the congruency
criteria
Explain, with clear, written steps, the
construction of a triangle, given 3
parameters that match one of the
congruency criteria
Identify which congruency criteria the
given triangle parameters match
Construct a triangle using given
parameters, with a rough diagram, fair
diagram and clear steps

Exercise questions from
Class VII textbook,
Practical Geometry
(Chapter 10)
Drawing a quadrilateral given 
five properties of the
quadrilateral
Just as a triangle requires a minimum of 3 
parameters to construct, invite students to
identify the minimum parameters
required to construct a quadrilateral (Hint:
break up the quadrilateral into two

triangles)
Building on the congruency criteria

covered for triangles, draw a rough
diagram for the given quadrilateral to
identify if it can be constructed.
Construct a quadrilateral with the given
parameters
Understand how a minimum of 5

parameters are required to construct a 
quadrilateral, by dividing it into two
triangles
Using a rough diagram, understand how
to construct the given quadrilateral
Construct a quadrilateral and write steps
to explain the construction
Textbook examples
Select questions from Ex
4.1, 4.2, 4.3, 4.4
Drawing a quadrilateral given 
less than 5 parameters
Discuss special cases where the known

properties of quadrilaterals can be used to
derive the minimum parameters required
to construct the quadrilateral
 Squares
 Rectangles
 Parallelograms (in general)
 Trapeziums
 Rhombus

 Kites
Understand properties of the following 
special quadrilaterals:

 Squares
 Rectangles
 Parallelograms (in general)
 Trapeziums
 Rhombus
 Kites
Use the known properties to construct a
quadrilateral even if less than 5
parameters are given (e.g. one
parameter is sufficient to construct a
square: side of the square)
Examples for each shape
Ex 4.5

Introduce exceptions to the 3 parameter/5 
parameter rules for triangles and
quadrilaterals by asking children to
construct figures that are not practically
possible (e.g. triangle given three angles, 
Understand that the minimum
parameter rule (3 for triangles and 5 for
quadrilaterals) may not be sufficient in
some cases
Draw a rough diagram using the
parameters given and analyse to see if


Feasibility of drawing the
given triangle/quadrilateral
Analyse constructions given
the following parameters
for quadrilaterals:
 Four angles and a side


quadrilateral given 3 sides and 2 nonincluded angles, etc.)
Deduce that 3 parameters are the

minimum number of parameters required
to construct a triangle but these may not
be sufficient in all cases. Similarly, deduce
that 5 parameters are the minimum
number of parameters required for
quadrilaterals but these may not be
sufficient in all cases.
Point out the importance of drawing a
rough diagram and analysing if a particular
triangle or quadrilateral can be
constructed with the given parameters
Activity
the parameters given are sufficient to
construct the figure
Explain with reason why a given set of
parameters is not sufficient to construct
a triangle or quadrilateral


3 sides, one included
angle and one nonincluded angle
2 sides, a diagonal,
two non-included
angles
Details below
Self-Assessment and Test
Why do we need to learn to construct geometrical shapes?
 We use various properties of parallel lines, triangles and quadrilaterals to construct these geometrical shapes. This process is a practical
reinforcement of various theoretical concepts. e.g. Understanding why three parameters are required to prove congruency of two triangles.
 Construction is fun!! Later on, this develops into advanced graphics techniques that have varied applications in architecture, engineering, animations,
etc.
Activity:
Children can choose to do one or more of the following:

Construction of geometrical designs using ruler and compass only (worksheet provided with various complex design patterns)

Scaled 2-D model of Poorna

Scaled 3-D model of Poorna
Self-Assessment:
Topic
Understanding of the topic
Working with simple cases
High comfort-level and confidence with the topic
Drawing a line
parallel to a given
line

I know the properties

used to construct parallel
lines.
I can construct a line parallel to the given line 
using the property and steps demonstrated
in class
I can construct a line parallel to the given line
using other properties of parallel lines (e.g.
other angle properties of transversal,
properties of parallelograms, etc.)
Drawing a triangle
given three
properties of the
triangle

I understand that the
parameters required to
construct a triangle are
the same as the criteria
required to prove
congruency of triangles
(SSS, ASA, SAS, RHS)

I can draw a rough diagram to indicate what 
parameters are given
I can construct a triangle with the given

parameters
I can write the steps required to construct
the triangle
I can identify if a triangle can be constructed
using the given parameters
I can explain why a triangle cannot be
constructed using the given parameters (e.g.
angle sum property is not satisfied, three
angles are not sufficient to construct a triangle,
etc.)
I can draw a rough diagram to indicate what 
parameters are given
I can construct a quadrilateral with the given 
parameters
I can write the steps required to construct
the quadrilateral
I can identify if a quadrilateral can be
constructed using the given parameters
I can explain why a quadrilateral cannot be
constructed using the given parameters (e.g.
which vertices cannot be located if four angles
and one side are given)
I can use properties of special quadrilaterals
(square, rectangle, parallelogram, trapezium,
rhombus, kite) to construct them even if fewer
than 5 parameters are given
Drawing a
quadrilateral given
five properties of
the quadrilateral




I understand that a

minimum of 5
parameters are required 
to construct a
quadrilateral

I can divide a
quadrilateral into two
triangles and use
properties of triangles to
understand how to
construct a quadrilateral

Uses of geometrical
constructions
I understand the practical
uses of geometrical
constructions and can cite
examples
I can use a ruler, compass and protractor to

draw a scaled version of simple 2-D objects e.g.
geometrical patterns like below
I can use a ruler and compass to draw a scaled
version of complex 2-D objects
e.g.

I can use a ruler, compass and protractor to
draw a scaled 2-D model of a simple 3-D shape
(e.g. a house)
Additional Comments: (Please write a few lines about your experience with the topic, whether you need to put in additional time or require teacher’s help,
etc. Be as specific as possible)