Topicmd3e0060f413ab448_1528449000663_0Topic

Triangles and their properties

Levelmd3e0060f413ab448_1528449084556_0Level

Second

Core curriculummd3e0060f413ab448_1528449076687_0Core curriculum

X. Polygons and circles. The student:

2) constructs a triangletriangletriangle having three sides and decides whether there it is possible to construct a triangle based on the triangle inequalitytriangle inequalitytriangle inequality theorem.

Timingmd3e0060f413ab448_1528449068082_0Timing

45 minutes

General objectivemd3e0060f413ab448_1528449523725_0General objective

Using and interpreting the representation. Using simple, well known mathematical objects, interpreting mathematical concepts and operating on mathematical objects.

Specific objectivesmd3e0060f413ab448_1528449552113_0Specific objectives

1. Investigating which line segments can create a triangle.

2. Recognising interior and exterior angles of the triangletriangletriangle.

3. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesmd3e0060f413ab448_1528450430307_0Learning outcomes

The student:

- examines which line segments can create the triangletriangletriangle,

- identifies interior and exterior angles of the triangle.

Methodsmd3e0060f413ab448_1528449534267_0Methods

1. Brainstorming.

2. Situational analysis.

Forms of workmd3e0060f413ab448_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmd3e0060f413ab448_1528450127855_0Introduction

The teacher introduces the topic of the lesson: revising what the triangletriangletriangle is checking if a triangle can be built of any three line segments and finding out what the interior and the exterior angles of the triangle are.

Task
Draw any ABC triangletriangletriangle.

What are the names of points A, B and C?

What are the names of the line segments AB, AC and BC?

Mark the interior angles of the triangletriangletriangle.

Task
Revise what supplementary angles are.

Proceduremd3e0060f413ab448_1528446435040_0Procedure

The teacher and the students give the definition of the exterior angle of the triangleexterior angle of the triangleexterior angle of the triangle.

Definition

- The exterior angle of the triangle is every angle that is supplementary to the interior angle of the triangle.md3e0060f413ab448_1527752263647_0- The exterior angle of the triangle is every angle that is supplementary to the interior angle of the triangle.

[Illustration 1]

β and γ are interior angles supplementary to angle ∝.

Task
Find the interior angles of the triangle if its exterior angles are 150°, 130° , 80°.

An extra task:
Can the exterior angles of the triangletriangletriangle be equal to ∝ = 100°, β = 90° , γ = 80°?

Task
Students work individually, using computers. Their task is to change the lengths of line segments and observe what the conditions under which it is possible to construct a triangle of three line segments.

[Geogebra applet]

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

- Do you think you can construct a triangletriangletriangle from any three line segments?

- When can you not construct a triangle?

- What relation between the lengths must hold to construct a triangle?

Students give the triangle inequalitytriangle inequalitytriangle inequality.

Theorem

- The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.md3e0060f413ab448_1527752256679_0- The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

From the line segments a, b and c you can construct a triangle if and only if:
$a<b+c,b<a+c,c<a+b$md3e0060f413ab448_1527752256679_0From the line segments a, b and c you can construct a triangle if and only if:
$a<b+c,b<a+c,c<a+b$

Task
Line segments a = 4 cm , b = 6 cm and c are the sides of a triangletriangletriangle. Can sidesideside c be equal to 1 cm?

Task
The sides of an isosceles triangle are 2 cm and 4 cm. Calculate the length of the third sidesideside.

Lesson summarymd3e0060f413ab448_1528450119332_0Lesson summary

Students do the revision exercises.

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

Definition

- The exterior angle of the triangleexterior angle of the triangleexterior angle of the triangle is every angle that is supplementary to the interior angle of the triangleinterior angle of the triangleinterior angle of the triangle.

[Illustration 2]

Theorem

- The sum of the lengths of any two sides of a triangle must be greater than the length of the third sidesideside.

From the line segments a, b and c you can construct a triangletriangletriangle if and only if:

Selected words and expressions used in the lesson plan

exterior angle of the triangleexterior angle of the triangleexterior angle of the triangle

interior angle of the triangleinterior angle of the triangleinterior angle of the triangle

sidesideside

triangletriangletriangle

triangle inequalitytriangle inequalitytriangle inequality