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Secondary 2E_Mathematics. Concept of Congruence (congruency). Welcome to the. 1 st E-learning 31 st January 2008. Instructions. Get your Mathematics notebook and worksheet ready before you proceed.
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Secondary 2E_Mathematics Concept of Congruence (congruency) Welcome to the 1st E-learning 31st January 2008
Instructions • Get your Mathematics notebook and worksheet ready before you proceed. • Read the text and logon to the assigned URLs for further information or work through the activities. • You may make your own notes on congruence in your Mathematics notebook. • Complete your work and hand in to your Mathematics teacher on Tuesday, 5th February 2008.
Let’s examine the properties of these shapes or figures! A B Q P R C • What do you notice about shape A, B and C after the A and C have moved? Do they fit onto another exactly? • What do you notice about shape P, Q and R after the P and R have moved? Do they fit onto another exactly?
Some concluding remarks: • Shape A fits shape B. Shape C does not fit shape A. • Shape P fits shape Q. Shape R does not fit shape P. We say that shape A “is congruent to” shape B. In mathematical notation, A B. • Similarly, shape P “is congruent to” shape Q. • In mathematical notation, P Q. • Note: the symbol for congruence is (3 equal straight lines) • Congruent figures (shapes) are identical, i.e. they have the same • shape, • size and • area and perimeter if the figures are closed.
2 object object image 3 object Let’s observe the motion of these shapes or figures! 1 Reflecting line/mirror image Rotation: both object & image are identical Reflection: both object & image are congruent Translation: both object & image fit each other exactly. image
Before you begin working on the solutions to the questions in the worksheet …
Read through the worksheet to get an overview of what is needed to complete the given task. • Logon onto the suggested URL/s given in each section. • Complete the set activities before attempting the questions.
A: Identify congruent figures through the various transformations. a) Logon to http://nlvm.usu.edu/en/nav/frames_asid_294_g_3_t_3.html?open=activities and try the three basic activities given. b) Click on first transform choose i) Reflection and any shape. Follow the instructions on the right panel to explore the properties. ii) Translation and any shape. Follow the instructions on the right panel to explore the properties. iii) Rotation and any shape. Follow the instructions on the right panel to explore the properties.
B, C & D: solving simple problems on congruent figures Before attempting to answer the questions in the worksheet, you are strongly advised to read and go through the activities in the suggested websites. a) Logon to http://regentsprep.org/Regents/math/congruen/Lcongruent.htm to learn about the definition of congruence. b) Click to learn more about congruency of triangles. c) go through L = Lesson, P = Practice on the same URL d)You could also logon to http://argyll.epsb.ca/jreed/math9/strand3/3203.htm, and read the sections on congruent triangles.
F: application of congruent figures logon to a) http://www.coolmath.com/tesspag1.htm to learn more about tessellation including some of the rules. Use the information to write your summary. b) http://www.mathsisfun.com/geometry/tessellation-artist.html to use the interactive Tessellation Artist workspace to create your tessellated pattern. Create your own pattern in your worksheet for submission.
Congratulations! You have come to the end of your e-lesson. @--|--- @--|--- Have a nice weekend!
