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Algebraic Manipulation
Arithmetic Problem Solving
Coordinate Geometry
Congruency
Distance, Midpoint and Circles
Expansion and Factorisation
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Pythagoras Theorem
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Circle Properties
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ACE
Statistical Poster Design
Graphing Calculator Design
Congruency
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Objectives:
At the end of this topic, you should
1. understand and identify congruent triangles by matching their corresponding sides and angles.
2. be able to state the conditions and prove for congruency in triangles.
Resources: Discovering Math Textbook 2A, Notes and Worksheets
Pretopic revision of angle properties:
Concept Mastery:
(1) Read Textbook 2A Pg 87 Section
4.1 A: Congruent Figures
. After reading, look at Example 1 and attempt "Try it 1".
(2) Continue to
B: Congruence and Transformation
. You need not do the class activities itself but you need to read the summary after each activity.
(3) Complete
Exercise 4.1
.
(4) Attempt this Quiz on Basic Concepts of Congruency:
http://www.quibblo.com/quiz/9IiygAQ/GeometryTestTwoCongruentTriangles
(5) Watch the following videos.
Video 1: Congruent Lines and Shapes  Definition
[URL:
http://www.youtube.com/watch?v=KtxdX34i3DQ
]
Video 2: Difference between Similarity & Congruency
[URL:
http://www.youtube.com/watch?v=P7mze8BuldE
]
Video 3: How to write the congruency statement with matching corresponding sides.
[URL:
http://www.youtube.com/watch?v=CUKDzC5f6B4&feature=fvsr
]
(6) Complete these Additional Practice Questions:
Congruency Worksheet 1 (questions only).pdf
Details
Download
99 KB
Solutions:
Congruency Worksheet 1 (with answers).pdf
Details
Download
117 KB
(7)
Attempt the ConcepTest:
http://spreadsheets.google.com/viewform?formkey=dEdIaFpfWjhncjdlMG5aTXFPT0Rub2c6MQ
Proving of Congruency
There are
4 rules
to determine whether 2 triangles are congruent:
SAS, ASA, SSS and RHS
.
SAS
: SideAngleSide [compare 2 sides and the
included
angle]
ASA
: AngleAngleSide [compare 2 angles and 1 other side]
SSS
: SideSideSide [compare 3 corresponding sides]
RHS
: RightangleHypotenuseSide [compare the hypotenuse and 1 other side provided triangle has a right angle]
You will be required to know all 4 rules and how to apply them to prove that 2 triangles are congruent.
Watch these videos to understand the proofs:
(1) SAS Rule  Understanding what it is
[URL:
http://www.youtube.com/watch?v=9Ntt4AzAJDs
]
(2) SAS Rule  How to use it
[URL:
http://www.youtube.com/watch?v=yQCvcunn3e0
]
(3) ASA Rule  Understanding what it is
[URL:
**http://www.youtube.com/watch?v=_zf0OqoPHgU&feature=channel**
]
(4) ASA Rule  How to use it
[URL:
**http://www.youtube.com/watch?v=GgfY66ldfrk**
]
(5) SSS Rule  Understanding what it is
[URL:
**http://www.youtube.com/watch?v=cjfXiXg7Nx4**
]
(6) SSS Rule  How to use it
[URL:
**http://www.youtube.com/watch?v=PKvIr20vmBE**
]
(7) All four rules together
[URL:
http://www.youtube.com/watch?v=pZZADeU3khw&feature=PlayList&p=C6FC3DA62DA6AC3C&playnext_from=PL&index=0&playnext=1
]
Video (8) More examples
[URL:
http://www.youtube.com/watch?v=5ZNAQ5Enx8I&feature=related
]
Why not SSA (sidesideangle)? Can SSA be used to prove Congruency?
Watch this video to see why...
[URL:
http://www.youtube.com/watch?v=wvYaFaMAwcc
]
HOWEVER.....there is a SPECIAL case of SSA which will work. This case involved a rightangled triangle. The rule is called RHS (rightangle, hypotenuse and 1 other side). The video below shows why. [Note that the video calls it the hypotenuseleg  we can call it RHS]
[URL:
http://www.youtube.com/watch?v=CuteD2Pg6YU
]
Solutions to Worksheets given out on Congruency & Similarity:
Congruency Worksheet Ex 1 Solutions.pdf
Details
Download
2 MB
Congruency Worksheet Ex 2 Solutions.pdf
Details
Download
1 MB
Congruency Worksheet Ex 3 Solutions.pdf
Details
Download
785 KB
Conditions for Similarity and Exercise Solutions.pdf
Details
Download
2 MB
Non Similar Triangles.pdf
Details
Download
112 KB
Non Similar Triangles Solutions (Full).pdf
Details
Download
2 MB
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At the end of this topic, you should
1. understand and identify congruent triangles by matching their corresponding sides and angles.
2. be able to state the conditions and prove for congruency in triangles.
Resources: Discovering Math Textbook 2A, Notes and Worksheets
Pretopic revision of angle properties: