Presentation on the topic circle. Presentation "circle and circle" presentation for a geometry lesson on the topic

Math lesson in 5th grade

on the topic "Circle and Circle".

• ©GBOU boarding school No. 1
• Mathematics teacher: Makarova N.A.
• St. Petersburg, 2015.

Goals and objectives of the lesson:

Educational:

• Ensure the understanding of the concepts of circle, circle and their elements (radius, diameter, chord, arc).
• Consider the relationship between the diameter and radius of a circle.
• Introduce the compass tool, teach how to draw a circle using a compass.
• Learn to find similarities and differences between a circle and a circle; broaden the horizons of students.

Educational:

• Development of logical thinking, attention, creative and cognitive abilities, imagination, ability to analyze, draw conclusions.
• Formation of accuracy and precision when making drawings.
• Application of information technologies in the study of mathematics.

Educational:

• Development of hard work, discipline, respect for classmates.
• Formation of interest in mathematics.

Equipment: interactive whiteboard, computer, drawing tools.

A compass is a drawing tool. It has a needle at one end and a pencil at the other.

You need to work with the compass carefully!!!

1. Mark a point in your notebook and name it the letter O.

2. Take a compass and spread the “legs” of the compass to a distance of 3 cm.

3. Place the needle of the compass at point O, and draw a closed line with the other “leg” of the compass.

A circle is a closed line consisting of points that are equally distant from the center.

Point O is called the center of the circle

Mark two points A and M on the circle.

Segments OA and OM are called radii of the circle.

The radius of a circle is the segment that connects the center of the circle and a point on the circle.

Let's connect the points O and M, O and A.

The radius is designated

Latin letter r.

Construct two circles with a radius of 2 cm in your notebook. Paint the inner area of ​​one circle.

CIRCLE is a geometric figure consisting of all points located at the same distance from the center of the circle.

CIRCLE is a geometric figure consisting of all points of the plane located inside the circle (including the circle itself).

Circle

Which objects are shaped like a circle and which ones are shaped like a circle?

Extend line segment AO until it intersects the circle.

Label the point of intersection with the letter K.

The segment AK is called the diameter of the circle.

The diameter of a circle is a line segment connecting two points on the circle and passing through its center.

The diameter is designated by the Latin letter d.

Connect the dots

M and K, A and M.

The segments MK and AM are called chords of the circle.

A chord is a line segment connecting two points on a circle.

Name all the radii, diameters and chords of a circle.

Draw a circle with center at point O.

Mark two points A and B on the circle.

Points A and B divided the circle into two parts, which are called arcs of the circle.

An arc of a circle is a part of a circle

between points A and B.

Name all the arcs on the circle:

Name the points

lying on a circle.

Name the points

not lying on the circle.

Name the points

lying on a circle.

Option 1

A1. What is the name of segment AB in drawing No. 1?

1) circle diameter

2) circle radius

3) chord of a circle

A2. Choose the correct continuation of the statement:

The radius of a circle is the segment that...

A3. Can a circle have two diameters of different lengths?

2) can't

3) make it difficult to answer

Option 2

A1. What is the name of segment AB in drawing No. 2?

1) chord of a circle

2) circle diameter

3) circle radius

A2. Choose the correct sentence of the statement:

The diameter of a circle is the segment that...

1) connects any two points on a circle

2) connects the center of the circle with any point on the circle

3) connects two points on a circle and passes through the center of the circle

A3. Can a circle have two radii of different lengths?

2) can't

3) find it difficult to answer

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Slide captions:

Name the shapes K E T S V A X

How many parts is the plane of the figure divided into?

Circle and circle Circle is a closed line Circle is a plane that lies inside the circle, together with the circle

Circle A circle divides a plane into two parts!

Construction O 1) Mark point O - the center of the circle. 2) Set the radius of the circle using a compass and ruler. 3) Place the leg of the compass at point O 4) Draw a circle.

All points of a circle are distant from its center. O – center of a circle and circle OA = OC = OE – radius – r AB – diameter - d AB = OA+OB d = 2r, r = d:2 O C A E B Radius – a segment connecting the center of the circle with a point lying on her. All radii of a circle are equal! Diameter is a segment connecting two points of a circle and passing through its center.

The diameter divides the circle into two semicircles, O C A B O C A B the circle into two semicircles.

Circular arc NE - arc NE, ends of the arc - points C and B. AC - arc AC, ends of the arc - points A and C. AB, BE O C A E B

Examples of a circle and a circle in life

Numbers for work: For consolidation of material: No. 850 (oral) No. 851 No. 853 No. 855 For repetition: No. 871(1) Independent work: No. 872(1)

Homework: paragraph 22, No. 874, No. 876, No. 878 (a, d, f)

No. 853 O A B r =3 cm OA= , OA r

No. 855 C D AC = 3cm, CB = 3cm D A = 4cm, B D =4cm B A

On the topic: methodological developments, presentations and notes

The image of a circle and its role in V. Nabokov’s story “The Circle”

"The 9 Circles of Hell According to Dante" A guide to the circles of hell from Dante Alighieri's The Divine Comedy.

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Slide captions:

Circle The presentation was prepared by: Kislova Svetlana Igorevna Mathematics teacher MBOU Secondary School No. 2 G. Lyskovo

Goals and objectives: Systematize theoretical material on the topic “Circle”. Improve problem solving skills. Prepare students for the test. Prepare students to successfully solve the Geometry module when passing the OGE.

properties of tangent C-tangent A-point of tangency C OA O A C a b M A B O

Theorem on tangent and secant C M A V The square of the length of a tangent is equal to the product of the secant and its external part. D C A B O The product of one secant and its external part is equal to the product of another secant and its external part M O

Central and inscribed angles Central Inscribed B A O D A C B O

An inscribed angle is either equal to half of its corresponding central angle, or (2) complements half of this angle to 180 degrees. 12

Properties of inscribed angles O A B D C B K A C

Property of intersecting chords C B K A D

Incircle Each point of the bisector of an undeveloped angle is equidistant from its sides. Conversely: each point lying inside the angle and equidistant from the sides of the angle lies on its bisector O O - intersection of bisectors Property of a bisector A B C D Property of a circumscribed quadrilateral AB+CD=BC+AD The sums of opposite sides are equal.

Circumscribed circle Each point of the perpendicular bisector to a segment is equidistant from the ends of this segment Conversely: each point equidistant from the ends of the segment lies on the perpendicular bisector to it O - intersection of perpendicular bisectors Property of the perpendicular bisector A D C B Property of the cyclic quadrilateral Sum of opposite angles is 180* O

Oral problems on finished drawings 160 Answer: 80 ? Answer: 45 B A C B C A D A B C M K R 5 6 3 Answer: 28 ?

A C B D 7 8 P=? Answer: 30 M K T O 70°? Answer: 20° O

Must be able to: Apply definitions, properties of figures, and various theorems when solving problems. Be able to build a logical chain of reasoning. Apply theory to a new situation.

120° 60° 120° 240° 115° 65° 230° 40° 140° 140° AC CB AB R KTP PK PT KPT - - 4 3 5 2 , 5 30° 4 8 60° - - Answers:

Group 2 1 2 3 4 B A B A Group 1 1 2 3 4 A B B D Group 3 1 2 3 4 B A ABC B

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CIRCLE AND CIRCLE

MATHEMATICS – 5th grade

Goals and objectives of the lesson:

Educational:

• Ensure the understanding of the concepts of circle, circle and their elements (radius, diameter, chord, arc).
• Consider the relationship between the diameter and radius of a circle.
• Introduce the compass tool, teach how to draw a circle using a compass.
• Learn to find similarities and differences between a circle and a circle; broaden the horizons of students.

Educational:

• Development of logical thinking, attention, creative and cognitive abilities, imagination, ability to analyze, draw conclusions.
• Formation of accuracy and precision when making drawings.
• Application of information technologies in the study of mathematics.

Educational:

• Development of hard work, discipline, respect for classmates.
• Formation of interest in mathematics.

Equipment: interactive whiteboard, computer, drawing tools.

A compass is a drawing tool. It has a needle at one end and a pencil at the other.

You need to work with the compass carefully!!!

1. Mark a point in your notebook and label it O.

2. Take a compass and spread the “legs” of the compass to a distance of 3 cm.

3. Place the needle of the compass at point O, and with the other “leg” of the compass, draw a closed line.

We got a closed line called circle . What is a circle?

Task No. 1: Which picture shows a circle and why.

Circle – a geometric figure consisting of all points located at the same distance from a given point. This point is called center of the circle .

Circle - This is the simplest of curved lines. One of the oldest geometric figures. Aristotle argued that planets and stars should move along the most perfect line - a circle. For hundreds of years, astronomers believed that planets moved in circles. Only in the 17th century did scientists: Copernicus, Galileo, Kepler, Newton refute this opinion.

Task 2

1) Draw a circle with center at point O.

2) Mark three points A, B and C on the circle.

3) Connect them with a segment to the center of the circle.

4) What can be said about the resulting segments?

Conclusion: All segments are equal, because all points of the circle are at the same distance from the center.

This distance is called radius, denoted by – r .

What is the radius of a circle?

Circle radius is a segment that connects the center of a circle and a point on the circle.

Even the Babylonians and ancient Indians considered the most important element of the circle to be - radius. The word is mathematical and means “ray”.

In ancient times this term did not exist. Euclid and other scientists simply said "straight from the center", then in the 11th century it was called "semi-diameter". The term "radius" was first used in 1569 by the French scientist Rams. “Radius” became generally accepted only in the 17th century.

Euclid -

Great Ancient Greek

mathematician; first

mathematician of Alexandria

schools

Construct two circles with a radius of 2 cm in your notebook. Paint the inner area of ​​one circle.

Circle

Circle

How are the two drawings similar and different?

CIRCLE - a geometric figure consisting of all points of a plane located inside a circle (including the circle itself).

CIRCLE – a geometric figure consisting of all points located at the same distance from the center of a circle.

Which objects are shaped like a circle and which ones are shaped like a circle?

Task 3

Construct a circle with a center at point O, r = 3 cm. Mark two points A and B on the circle and connect them with a segment.

AB – chord

Chord – a segment connecting two points on a circle.

Chord - this is the Greek word “horde” - string, which was introduced by European scientists in the 12-13th centuries. A chord divides a circle into two arcs.

СD = r+r = 2r = d = 2r "width="640"

Task 4

Draw a chord through the center of the circle.

This chord is called - diameter, denoted by – d.

Define diameter.

Circle diameter is a chord passing through the center of the circle.

СD = OS+ОD, OS = r, ОD = r = СD = r+r = 2r = d = 2r

• The diameter is made up of two radii, so the diameter is twice as long as the radius. And the radius is 2 times smaller than the diameter.
• So, diameter is equal to 2 radii, and then the radius is half the diameter. r = 4 cm, d=2 r, d = 2 4 = 8 cm d = 8 cm, r=d:2, r = 8:2 = 4 cm
• Remember these formulas!

d=2 ·r

How are radius and diameter related?

Extend line segment AO until it intersects the circle.

Label the point of intersection with the letter K.

Section AK is called diameter circles.

Diameter denoted by a Latin letter d.

Circle diameter is a segment connecting two points on a circle and passing through its center.

Connect the dots

M and K, A and M.

The segments MK and AM are called chords circles.

Chord is a line segment connecting two points on a circle.

Name all the radii, diameters and chords of a circle.

Draw a circle with center at point O.

Mark two points A and B on the circle.

Points A and B divided the circle into two parts, which are called arcs circles.

State the definition of an arc circles.

Arc of a circle - this is the part of the circle enclosed between two of its points.

Name all the arcs on the circle:

points,

lying on a circle.

points,

not lying on the circle.

points,

lying on a circle.

Test

Option 2

A1. What is the name of segment AB in drawing No. 2?

1) chord of a circle

2) circle diameter

3) circle radius

A2. Choose the correct sentence of the statement:

The diameter of a circle is the segment that...

A3. Can a circle have two radii of different lengths?

2) can't

3) find it difficult to answer

Option 1

A1. What is the name of segment AB in drawing No. 1?

1) circle diameter

2) circle radius

3) chord of a circle

A2. Choose the correct continuation of the statement:

The radius of a circle is the segment that...

1) connects any two points on a circle

2) connects the center of the circle with any point on the circle

3) connects two points on a circle and passes through the center of the circle

A3. Can a circle have two diameters of different lengths?

2) can't

3) make it difficult to answer

check yourself

Draw a circle with a center at point O and a radius of 3 cm. Draw a straight line that intersects the circle at points M and K.

At what distance from the center of the circle are these points?

Segments OM and OK are radii of a circle, therefore

OM=3 cm, OK=3 cm

Solution

Answer: at a distance of 3 cm

Task No. 1

• Given a segment AB, its length is 4 cm. Construct point X if it is known that AX = 3 cm, BX = 5 cm.

How many points did you get?

Solution

Answer: two dots

Task No. 2

• The segment AB is the same as in the previous task, its length is 4 cm. Construct point X if it is known that: 1) AX = 1 cm, BX = 3 cm. 2) AX = 1 cm, BX = 2 cm. How many points did you get in the first case and how many in the second case?

Solution

Answer: none!

Answer: one point

Task No. 3

The radius of the circle with center O is 2 cm. Position points A, B, C so that: the distance from O to A is less than 2 cm, the distance from O to B is 2 cm, the distance from C to O is more than 2 cm.

Solution

2 cm

Answer: point A can be located anywhere inside the circle; point B – on the circle; point C – anywhere outside the circle

Lesson summary (reflection):

Describe your impressions about today's lesson:

• I found out…
• I can…
• It was difficult…
• I like it…
• Thanks for…

Homework

• pp. 133-134, memo (learn definitions),
• Ex. 855, 874, 875, 876.
• Extra . Make a pattern of circles (ornament).

Thanks to all get to work!

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Slide captions:

Grade 5 "Circle and circle"

Mental arithmetic Calculate:

Oral counting On the first day, 9 rows of currants were planted, 7 bushes in each row. How many currant bushes were planted on the first day?

Mental calculation How many times is 4 hours less than a day? How many times is 40 m less than 1 km?

Mental calculation How many times is a journey of 36 km longer than a journey of 4 km?

What types of lines are shown in the figure?

CIRCLE CIRCLE

My compass, the dashing circus performer, draws a circle with one foot, and pierces the paper with the other, clings on and doesn’t take a step.

Draw a circle in your notebook. Task No. 1.

O R t. O - center of the circle O R - radius or r A R - diameter or d radius diameter A d = 2r r = d: 2

A B C D E F K L O r - radius d - diameter List all radii and diameters

A circle is a closed line, all points of which are at the same distance from a given point. This point is called the center of the circle. A circle is a part of a plane that lies inside a circle (along with the circle itself). Radius is a segment connecting the center of a circle to a point on the circle. All radii of a circle are equal to each other. Diameter is a segment connecting two points on a circle and passing through the center of the circle. All diameters of a circle are equal to each other. The most important.