Topicm486a6cbdded3d14b_1528449000663_0Topic

Congruence of figures

Levelm486a6cbdded3d14b_1528449084556_0Level

Second

Core curriculumm486a6cbdded3d14b_1528449076687_0Core curriculum

XI. Calculations in geometry. The student:

7) calculates the angles using the known properties of angles and polygons.

Timingm486a6cbdded3d14b_1528449068082_0Timing

45 minutes

General objectivem486a6cbdded3d14b_1528449523725_0General objective

Noticing regularities, similarities and analogies and formulating relevant conclusions.

Specific objectivesm486a6cbdded3d14b_1528449552113_0Specific objectives

1. Recognising and drawing congruent figurescongruent figurescongruent figures.

2. Finding images of figures in symmetry about a pointpointpoint and axial symmetryaxial symmetryaxial symmetry.

Learning outcomesm486a6cbdded3d14b_1528450430307_0Learning outcomes

The student:

- define congruent figures, recognises congruent figurescongruent figurescongruent figures

- find images of figures in symmetry about a pointpointpoint and axial symmetryaxial symmetryaxial symmetry.

Methodsm486a6cbdded3d14b_1528449534267_0Methods

1. Practical exercises.

2. Situational analysis.

Forms of workm486a6cbdded3d14b_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm486a6cbdded3d14b_1528450127855_0Introduction

The teacher introduces the topic of the lesson: how to recognise congruent figurescongruent figurescongruent figures and how to find images of figures in symmetry about a pointpointpoint and axial symmetryaxial symmetryaxial symmetry.

Task

There are two rectangles - first whose sides are equal to 2 cm and 4 cm and second whose sides are equal to 4 cm and 6 cm. Are they the same?

Procedurem486a6cbdded3d14b_1528446435040_0Procedure

Task
Find an image of ABC triangle in symmetry about axis p. Does the obtained triangle have the same size and shape as ABC triangle?

Task
Find an image of ABC triangle in symmetry about pointpointpoint A. Does the obtained triangle have the same size and shape as ABC triangle?

The teacher and the students give the definition.

Definition

- Figures that have the same shape and size are called congruent.m486a6cbdded3d14b_1527752263647_0- Figures that have the same shape and size are called congruent.

An image of a figurefigurefigure in symmetry about a pointpointpoint is a congruent figure.

An image of a figure in axial symmetryaxial symmetryaxial symmetry is a congruent figurefigurefigure.

Task
Find an image of a circlecirclecircle whose radius is 4 cm, with respect to line p.

Ale the circlecirclecircle and its image congruent?

Two circles are congruent if they have the same radius.

Two line segments are congruent if and only if they are the same length.

Definition

- Two angles of the same measure are congruent.m486a6cbdded3d14b_1527752256679_0- Two angles of the same measure are congruent.

Task
Choose pairs of congruent anglescongruent anglescongruent angles.

[Illustration 1]

Task
Students work individually, using computers. Their task is to observe how the image of the blue polygon changes when we change the location of the axis of symmetry.

[Geogebra applet]

Having completed the exercise, they present the results of their observations by answering the following questions:

- How the image of the blue polygon changes when we change the location of the axis of symmetry of the polygons?

- Can you locate the apexes of the blue polygon in such a way that they overlay the apexes of the green polygon?

Definition

- Polygons are congruent when all corresponding sides and interior angles are congruent.m486a6cbdded3d14b_1527712094602_0- Polygons are congruent when all corresponding sides and interior angles are congruent.

[Illustration 2]

Polygons are congruent if and only if all corresponding interior angles have the same measure and all corresponding sides are the same length.

Task
The area of the ABCD rectanglerectanglerectangle is equal to 20 cmIndeks górny 2² and one of its sides is equal to 5 cm. Calculate the perimeter of the EFGH rectangle which is congruent to the ABCD rectanglerectanglerectangle.

An extra task:
Parallelograms ABCD and EFGH are congruent. The perimeter of the ABCD parallelogram is equal to 30 cm. Side EF of the EFGH parallelogram is 2 cm shorter than the side FG. Calculate the lengths of the sides of the ABCD parallelogram.

Lesson summarym486a6cbdded3d14b_1528450119332_0Lesson summary

Students do the revision exercises.

Then together they sum‑up the classes, by formulating the conclusions to remember.

- Figures that have the same shape and size are called congruent.

- An image of a figure in symmetry about a pointpointpoint is a congruent figurefigurefigure.

- An image of a figurefigurefigure in axial symmetryaxial symmetryaxial symmetry is a congruent figure.

- Two circles are congruent if they have the same radius.

- Two line segments are congruent if and only if they are the same length.

- Two angles of the same measure are congruent.

- Polygons are congruent when all corresponding sides and interior angles are congruent.

- Polygons are congruent if and only if all corresponding interior angles have the same measure and all corresponding sides are the same length.

Selected words and expressions used in the lesson plan

axial symmetryaxial symmetryaxial symmetry

circlecirclecircle

congruent anglescongruent anglescongruent angles

congruent figurescongruent figurescongruent figures

congruent polygonscongruent polygonscongruent polygons

figurefigurefigure

line segmentline segmentline segment

pointpointpoint

rectanglerectanglerectangle

symmetric figuressymmetric figuressymmetric figures