Topicm935017da5354fe0f_1528449000663_0Topic

Trapezoids and their properties

Levelm935017da5354fe0f_1528449084556_0Level

Second

Core curriculumm935017da5354fe0f_1528449076687_0Core curriculum

X. Polygons. The student:

2) apply formulas to the area of a triangle, a rectangle, a square, a parallelogram, a rhombus, a trapezoid, and to determine the length of sections with a difficulty level not greater than in the examples:

a) calculate the shortest rectangular triangle with sides of 5 cm, 12 cm and 13 cm long,

b) ABCD diamond diagonals have the length AC = 8 dm and BD = 10 dm. The diagonal BD of the diamond has been extended to point E in such a way that the section BE is twice as long as this diagonal. Calculate the field of the CDE triangle (the task has two answers).

Timingm935017da5354fe0f_1528449068082_0Timing

45 minutes

General objectivem935017da5354fe0f_1528449523725_0General objective

Noticing regularities, similarities and analogies and formulating relevant conclusions.

Specific objectivesm935017da5354fe0f_1528449552113_0Specific objectives

1. Recognising, drawing and using the properties of trapezoids.

2. Calculating the areaareaarea and the perimeter of a trapezoidperimeter of a trapezoidperimeter of a trapezoid.

3. Communicating in English, developing basic mathematical, computer and scientific competences, shaping the ability to learn.

Learning outcomesm935017da5354fe0f_1528450430307_0Learning outcomes

The student:

- recognises, draws and uses the properties of trapezoids,

- calculates the area and the perimeter of a trapezoid.

Methodsm935017da5354fe0f_1528449534267_0Methods

1. Practical exercises.

2. Analysis of the situation.

Forms of workm935017da5354fe0f_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm935017da5354fe0f_1528450127855_0Introduction

The teacher informs the students that during this lesson they will revise what a trapezoid is. They will also get familiar with the properties of the trapezoidtrapezoidtrapezoid and the formulas for calculating the areaareaarea and the perimeterperimeterperimeter of the trapezoid.

Task
The teacher divides the class into groups of 4‑5 students and distributes various tetragons cut out of coloured paper (which are not parallelograms). The students have to select those which are trapezoids.

Procedurem935017da5354fe0f_1528446435040_0Procedure

The groups prepare the answers to the following questions:

- What kind of tetragon is called a trapezoidtrapezoidtrapezoid?
- How do we call the sides of the trapezoid?
- Which trapezoid is called isosceles?
- What kind of properties does an isosceles trapezoidisosceles trapezoidisosceles trapezoid have?
- What kind of trapezoid do we call the right‑angled trapezoidright‑angled trapezoidright‑angled trapezoid?
- Where is the altitudealtitudealtitude of an isosceles trapezoid?
- How to calculate the perimeter of a trapezoidperimeter of a trapezoidperimeter of a trapezoid?
- What is the formula for the area of a trapezoid?

Students can search for information in the Internet. After a few minutes the representatives of each group answer the questions.

Definition
If a tetragon has at least one pair of parallel sides, it is called a trapezoid.
The parallel sides of a trapezoid are called its bases and the remaining two sides are referred to as the legs.m935017da5354fe0f_1527752256679_0If a tetragon has at least one pair of parallel sides, it is called a trapezoid.
The parallel sides of a trapezoid are called its bases and the remaining two sides are referred to as the legs.

The teacher tells the students that during this lesson they will discuss trapezoids which have exactly one pair of parallel sides.

Definition
A trapezoidtrapezoidtrapezoid whose legs are equal and is not a parallelogram is called an isosceles trapezoid.

In an isosceles trapezoidisosceles trapezoidisosceles trapezoid:

- the diagonals are equal,

- the base angles have the same measuremeasuremeasure.

Definition
A trapezoid which has at least one right angle is called a right‑angled trapezoid.
In a right‑angled trapezoid, the leg perpendicular to the base is also its altitude.m935017da5354fe0f_1527712094602_0A trapezoid which has at least one right angle is called a right‑angled trapezoid.
In a right‑angled trapezoid, the leg perpendicular to the base is also its altitude.

The sum of adjacent angles at the same leg is equal 180°.

The perimeter of a trapezoidperimeter of a trapezoidperimeter of a trapezoid is the sum of the lengths of all its sides.

The area of a trapezoid, where the base is a, b and the altitude is h, is expressed with the following formula:m935017da5354fe0f_1527752263647_0The area of a trapezoid, where the base is a, b and the altitude is h, is expressed with the following formula:

Task
The teacher asks the students to divide the selected trapezoids into isosceles, right‑angles and trapezoids which are neither isosceles nor right‑angled trapezoids.

Task
The teacher asks the students to measuremeasuremeasure the sides and calculate the perimeterperimeterperimeter of three selected trapezoids.

Task
Draw a trapezoid whose upper base equals 4 cm, the lower base equals 6 cm and its legs have the lengths of 3 cm and 5 cm.

Task
Students work individually, using computers. Their task is to determine two angles of a trapezoidtrapezoidtrapezoid on the basis of the given measures of the remaining angles.

Calculating the measures of the angles:

[Geogebra applet]

Task
Calculating the area of an isosceles trapezoid whose one base equals 4 cm and the other is twice as long. The altitude of the trapezoid is by 2 cm shorter than the length of the leg and the perimeter of the trapezoid equals 34 cm.

An extra task
Calculating the area of a trapezoid whose one base is equal to 6 cm, the other is 2 cm longer and the altitude is equal to 70% of the longer base.

Lesson summarym935017da5354fe0f_1528450119332_0Lesson summary

Students do the revision exercises. Then, they together sum up the classes by formulating conclusions to memorise.

If a tetragon has at least one pair of parallel sides, it is called a trapezoidtrapezoidtrapezoid.

The parallel sides of a trapezoid are called the bases and the remaining two sides are the legs.

A trapezoid whose legs are equal and which is not a parallelogram is called an isosceles trapezoidisosceles trapezoidisosceles trapezoid.

In an isosceles trapezoid:
- the diagonals are equal,
- the base angles have the same measuremeasuremeasure.

A trapezoid which has at least one right angle is called a right‑angled trapezoidright‑angled trapezoidright‑angled trapezoid.

In a right‑angled trapezoid, the leg which is perpendicularperpendicularperpendicular to the base is also called its altitudealtitudealtitude.

The sum of angles adjacent to the same leg is equal 180°.

The perimeter of a trapezoidperimeter of a trapezoidperimeter of a trapezoid is the sum of the lengths of its all sides.

The areaareaarea of a trapezoid with the base is a, b and the altitude h is expressed with the following formula:

Selected words and expressions used in the lesson plan

altitudealtitudealtitude

areaareaarea

isosceles trapezoidisosceles trapezoidisosceles trapezoid

measuremeasuremeasure

perimeterperimeterperimeter

perpendicularperpendicularperpendicular

right‑angled trapezoidright‑angled trapezoidright‑angled trapezoid

area of a trapezoidarea of a trapezoidarea of a trapezoid

perimeter of a trapezoidperimeter of a trapezoidperimeter of a trapezoid

trapezoidtrapezoidtrapezoid