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

Pre-topic 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/Geometry-Test-Two-Congruent-Triangles

(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:

Solutions:

(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: Side-Angle-Side [compare 2 sides and the included angle]
ASA: Angle-Angle-Side [compare 2 angles and 1 other side]
SSS: Side-Side-Side [compare 3 corresponding sides]
RHS: Right-angle-Hypotenuse-Side [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 (side-side-angle)? 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 right-angled triangle. The rule is called RHS (right-angle, hypotenuse and 1 other side). The video below shows why. [Note that the video calls it the hypotenuse-leg - we can call it RHS]

[URL: http://www.youtube.com/watch?v=CuteD2Pg6YU]


Solutions to Worksheets given out on Congruency & Similarity: