Download Chapter 7: Congruence of Triangles

7 Congruence of Triangles
Objectives:
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Understand the meaning of congruence and how it applies to geometrical shapes
Identify congruence in line segments, angles and plane figures
Understand the criteria for congruence in triangles and use them to identify congruent triangles
Understand the concept of similarity as against congruency
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Differentiate between similar and congruent triangles
Before We Begin:
Terms
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Line segment
Angle
Triangle
Vertices of a triangle
Sides of a triangle
Right-angled triangle
Hypotenuse
Symbols/ Notations
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Point A
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∠Y
ΔPQR
Methods
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Measure the length of a line using a ruler
Draw a line of given length using a ruler
Measure an angle using a protractor
Draw an angle using a protractor and ruler
Lesson Plan: (Chapter 7 from last year's textbook - Mathematics for Class VII, CBSE)
Content
7.1, 7.2 Introduction
Teacher's Activity
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Student's Activity
Introduce the term "congruency" Provide examples of congruent shapes
and explain how it is a
around them
geometrical term for "sameness"
in shape and size
Explain how superimposing
objects is a simple technique for
testing congruency of plane
figures
Assignments
7.3, 7.4 Congruent Lines and
Angles
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Ask children to point out
examples of congruent shapes
around them
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Draw out examples of lines and
angles on the board
Invite students to explain how
they would test for congruency
(other than superimposing)
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Deduce the rules for testing congruency
in lines and angles
Explain the various criteria for
congruency of triangles (SSS,
SAS, ASA, RHS)
Solve examples to prove
congruency of triangles
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Using the various criteria for
Ex 7.1, 7.2
congruency, determine if two given
triangles are congruent
Find missing angles or sides for
congruent triangles
Solve real-world problems to understand
the application of congruency
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7.5, 7.6 Congruence of Triangles 
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Similar Shapes
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Similar Triangles
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Real-world examples
Self-assessment and Test
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Introduce the definition of
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"similarity" in geometrical
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shapes as sameness in shape but
not in size
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Provide examples of similar
shapes that are not congruent
Identify similar shapes around them
Explain why a given shape is similar but
not congruent
Understand that all congruent shapes
are also similar
Problems from NIOS/IG
textbooks
Explain the concept of
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proportionality for sides of
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triangles
Explain the various criteria to
determine similarity in triangles
(AAA, SSS, SAS)
Identify triangles that are similar
Solve for missing sides or angles of
similar triangles
Problems from NIOS/IG
textbooks
Explain, through examples, how 
congruency and similarity of
triangles can be used in realworld situations
Understand how congruency and
similarity of triangles can be used in realworld situations
Why do we need to learn about Congruency?
e.g. Bridges (congruent triangles form a good support structure); Creating multiple items that are identical (e.g. notebooks, paintings, etc)
Sample real-world problem: The map below shows five different towns. The town of Meridian was given its name because it lies exactly halfway between two pairs of cities:
Camden and Grenata, and Lowell and Morsetown.
Using the information in the map, what is the distance between Camden and Lowell?
Why do we need to learn about Similarity?
e.g. Calculating the height of objects that are difficult to measure.
Using shadows is a quick way to estimate the heights of trees, flagpoles, buildings, and other tall objects. To begin, pick an object whose height may be impractical to measure,
and then measure the length of the shadow your object casts. Also measure the shadow cast at the same time of day by a yardstick (or some other object of known height)
standing straight up on the ground. Since you know the lengths of the two shadows and the length of the yardstick, you can use the fact that the sun's rays are approximately
parallel to set up a proportion with similar triangles.
Because the sun's rays are parallel, the triangles are similar. Thus:
Self-Assessment:
Topic
Understanding of the topic
Working with simple cases
High comfort-level and confidence with the
topic
Congruency
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I know the geometrical meaning of the
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word "congruent" and I can give examples
of congruent shapes around me
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I can determine if two lines or two angles 
are congruent
I can determine if two triangles are
congruent by superimposing one on the 
other
I can determine if two triangles are congruent
by using one of the criteria for congruency
(SSS, SAS, ASA, RHS)
I can use the congruence property of triangles
to find missing angles or sides
Similarity
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I know the geometrical meaning of the
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word "similar" and I can give examples of
similar shapes around me
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I can determine if sides of a triangle are
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proportional (in a ratio)
I can determine if two triangles are similar
by measuring their angles and sides
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I can determine if two triangles are similar by
using one of the criteria for similarity (AAA,
SSS, SAS)
I can use the similarity property of triangles
to find missing angles or sides
Real-world
application
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I can give examples of congruent and
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similar shapes in the real world
I know the difference between congruent
and similar shapes and can explain why a
shape is similar but not congruent
I can provide examples of how congruent 
and similar triangles can be used to solve
real-world problems
I can solve real-world problems involving
congruent and similar triangles and solve for
missing lengths and angles
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