Topicm93145c2f9fcb19c1_1528449000663_0Topic

The Converse of Pythagorean Theoremconverse of Pythagorean theoremConverse of Pythagorean Theorem

Levelm93145c2f9fcb19c1_1528449084556_0Level

Second

Core curriculumm93145c2f9fcb19c1_1528449076687_0Core curriculum

VIII. Properties of planar geometric figures. The student:

- knows and uses the converse of Pythagorean theorem in practical situations.

Timingm93145c2f9fcb19c1_1528449068082_0Timing

45 minutes

General objectivem93145c2f9fcb19c1_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm93145c2f9fcb19c1_1528449552113_0Specific objectives

1. Formulating the converse of Pythagorean theoremconverse of Pythagorean theoremconverse of Pythagorean theorem. Checking if a triangletriangletriangle with given sides is right‑angled.

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

Learning outcomesm93145c2f9fcb19c1_1528450430307_0Learning outcomes

The student:

- formulates the converse of Pythagorean theoremconverse of Pythagorean theoremconverse of Pythagorean theorem,

- cecks, if a triangletriangletriangle with given sides is right‑angled.

Methodsm93145c2f9fcb19c1_1528449534267_0Methods

1. Discussion.

2. Flipped classroom method.

Forms of workm93145c2f9fcb19c1_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm93145c2f9fcb19c1_1528450127855_0Introduction

The teachers asks the students to revise the following material at home deriving a theorem, the types of theorems, the Pythagorean theoremPythagorean theoremPythagorean theorem and Pythagorean triples.

Task
Students revise the Pythagorean theorem and its main applications.

Procedurem93145c2f9fcb19c1_1528446435040_0Procedure

Students discuss how to derive a converse theorem and what the difference is between a converse and an inverse theorem as well as whether the converse theorem is always true. The students provide examples. The conclusion of the discussion should be the formulation of the converse of the Pythagorean theoremPythagorean theoremPythagorean theorem.

The converse of Pythagorean theoremconverse of Pythagorean theoremconverse of Pythagorean theorem:

If numbers a, b, c, which are the lengths of the triangle (c being the longest side of the triangle), fulfil the condition:
$a^2+b^2=c^2$
then the triangle is a right‑angled triangle.m93145c2f9fcb19c1_1527752263647_0If numbers a, b, c, which are the lengths of the triangle (c being the longest side of the triangle), fulfil the condition:
$a^2+b^2=c^2$
then the triangle is a right‑angled triangle.

Task
Students check, if the triangle whose sides are:

a) $8,15,17$,

b) $\sqrt{3},\sqrt{4},\sqrt{5}$,

is right‑angled.

Task
Students work individually using computers. Their task is to check for which m number the given sides are the sides of a right‑angled triangletriangletriangle.

[Geogebra applet]

Task
Students check, if a triangletriangletriangle whose sides are 2x, 3x, 5x is a right‑angled triangleright‑angled triangleright‑angled triangle.

Task
There are line segments whose lengths are $3\sqrt{2}$ and $2\sqrt{3}$. Students calculate the length of the third line segment so that they can build a right‑angled triangleright‑angled triangleright‑angled triangle out of these line segments.

Task
The sides of a Pythagorean triangletriangletriangle have the following lengths $n$, $\frac{n^2-1}{2}$, $\frac{n^2+1}{2}$, where n is a natural, odd number greater than 1. Students find the perimeter of the triangle for $n=3$.

An extra task:
Students check, if the parallelogram, whose sides are 3 and 5 cm and the diagonal is 8 cm, is a rectangle.m93145c2f9fcb19c1_1527752256679_0check, if the parallelogram, whose sides are 3 and 5 cm and the diagonal is 8 cm, is a rectangle.

Lesson summarym93145c2f9fcb19c1_1528450119332_0Lesson summary

Students do extra exercises.

Selected words and expressions used in the lesson plan

cathetusecathetusecathetuse

converse of Pythagorean theoremconverse of Pythagorean theoremconverse of Pythagorean theorem

egyptian triangleegyptian triangleegyptian triangle

hypotenusehypotenusehypotenuse

Pythagorean theoremPythagorean theoremPythagorean theorem

pythagorean triplepythagorean triplepythagorean triple

right‑angled triangleright‑angled triangleright‑angled triangle

triangletriangletriangle