Topicm881c0e34b455bfb7_1528449000663_0Topic

Pythagorean TheoremPythagorean theoremPythagorean Theorem III

Levelm881c0e34b455bfb7_1528449084556_0Level

Second

Core curriculumm881c0e34b455bfb7_1528449076687_0Core curriculum

VIII. Properties of planar geometric figures. The student:

8) knows and uses the Pythagorean theoremPythagorean theoremPythagorean theorem (without the converse theorem) in practical situations.

Timingm881c0e34b455bfb7_1528449068082_0Timing

45 minutes

General objectivem881c0e34b455bfb7_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm881c0e34b455bfb7_1528449552113_0Specific objectives

1. Application of the Pythagorean theoremPythagorean theoremPythagorean theorem in geometric exercises.

2. Calculating the lengths of line segments in polygons using the Pythagorean theoremPythagorean theoremPythagorean theorem.

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

Learning outcomesm881c0e34b455bfb7_1528450430307_0Learning outcomes

The student:

- applies the Pythagorean theoremPythagorean theoremPythagorean theorem in geometric exercises,

- calculates the lengths of line segments in polygons using the Pythagorean theoremPythagorean theoremPythagorean theorem.

Methodsm881c0e34b455bfb7_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workm881c0e34b455bfb7_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm881c0e34b455bfb7_1528450127855_0Introduction

The teacher informs students that during this class they will learn to apply the Pythagorean theoremPythagorean theoremPythagorean theorem in geometric exercises.

Task
Students revise the Pythagorean theoremPythagorean theoremPythagorean theorem.

The teacher divides the class into groups 4‑5 people. Each group does the same exercise set previously prepared by the teacher. Then, the students discuss the solutions to the exercises.

Procedurem881c0e34b455bfb7_1528446435040_0Procedure

Task
a) Calculate the length of the diagonal of the square whose side is 5 cm.

b) Calculate the length of the side of the square whose diagonal equals $\sqrt{2}$ cm.

Task
Calculate the length of the diagonal of the rectangle whose sides are 6 cm and 8 cm.

Task
Calculate the perimeter of a rhombus whose diagonals are 10 cm and 14 cm.

Task
In a right‑angled triangle one cathetuse is twice as long as the other one and the hypotenuse is 16 cm. Calculate the perimeter of the triangle.m881c0e34b455bfb7_1527752256679_0In a right‑angled triangle one cathetuse is twice as long as the other one and the hypotenuse is 16 cm. Calculate the perimeter of the triangle.

Task
Students work individually using computers. Their task is to compare the sums of the areas of squares built on the opposite sidesopposite sidesopposite sides of a tetragon. The result of the observations should be the formulation of the properties of the sides of the deltoiddeltoiddeltoid.

[Geogebra applet]

In deltoids the sums of the squares of the opposite sides are equal.m881c0e34b455bfb7_1527752263647_0In deltoids the sums of the squares of the opposite sides are equal.

Students who are interested into mathematics can prove this theorem at home.

An extra task:
Students calculate the perimeter of the regular octagon that was created by cutting off the corners of a square whose side is 8 cm.

Lesson summarym881c0e34b455bfb7_1528450119332_0Lesson summary

Students do the revision exercises.

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

Pythagorean theoremPythagorean theoremPythagorean theorem.

- If a and b are the lengths of the cathetuses and c is the length of the hypotenuse in a right‑angled triangle then:

Selected words and expressions used in the lesson plan

cathetusecathetusecathetuse

deltoiddeltoiddeltoid

hypotenusehypotenusehypotenuse

opposite sidesopposite sidesopposite sides

Pythagorean theoremPythagorean theoremPythagorean theorem

Pythagorean triplePythagorean triplePythagorean triple