Secondary 2E_Mathematics

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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
• 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.

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

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.