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Presentation on the theme of the circle. presentation for a lesson in geometry (grade 9) on the topic |
To use the preview of presentations, create a Google account (account) and sign in: https://accounts.google.com Slides captions:Grade 5 "Circle and circle" Mental Count Calculate: Oral count 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 Counting How many times longer is a 36 km journey than a 4 km journey? What types of lines are shown in the figure? CIRCLE CIRCLE My compass, dashing circus performer, Draws a circle with one foot, And the other pierced the paper, Caught on and - not a step. Draw a circle in your notebook. Task number 1. O R t. O - center of the circle O R - radius or r A R - diameter or d radius diameter A d \u003d 2r r \u003d 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 (together with the circle itself). A radius is a line segment that connects the center of a circle to a point on the circle. All radii of a circle are equal to each other. Diameter is a line segment that connects two points on a circle and passes through the center of the circle. All circle diameters are equal to each other. The most important. Attention! The slide preview is for informational purposes only and may not represent the full extent of the presentation. If you are interested in this work, please download the full version. The first lesson in the topic "Ordinary fractions". Textbook by N.Ya. Vilenkin “Mathematics 5”. The objectives of the lesson: to familiarize students with the concept of a circle and a circle; the formation of the ability to build a circle using a compass for a given radius and diameter. Learning objectives aimed at achieving: Personal development:
Meta-subject development:
Subject development:
Type of lesson: a lesson in obtaining new knowledge, skills and abilities. Forms of student work:
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Structure and course of the lesson
To use the preview of presentations, create a Google account (account) and sign in: https://accounts.google.com Slides captions:Name the figures K E T S B A X Into how many parts is the plane of the figure divided? Circle and circle Circle - a closed line Circle - a plane that lies inside the circle, together with the circle Circle A circle divides a plane into two parts! Construction of O 1) We mark the point O - the center of the circle. 2) Set the radius of the circle using a compass and ruler. 3) We set the leg of the compass at points O 4) We draw a circle. All points of the circle are removed from its center. O - the center of the circle and the circle OA \u003d OS \u003d OE - radius - r AB - diameter - d AB \u003d OA + OB d \u003d 2r, r \u003d 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 line segment that connects two points on a circle and passes through its center. The diameter divides the circle into two semicircles, O C A B O C A B the circle into two semicircles. Arc of a circle CB - arc CB, 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 fixing the material: No. 850 (orally) No. 851 No. 853 No. 855 For repetition: No. 871 (1) Independent work: No. 872 (1) Homework: item 22, No. 874, No. 876, No. 878 (a, d, e) No. 853 O A B r \u003d 3 cm OA \u003d, 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 notesThe image of the circle and its role in the story of V. Nabokov "Circle" "9 circles of hell according to Dante" A guide to the circles of hell from the "Divine Comedy" by Dante Alighieri. The Divine Comedy (Italian: La Commedia, later La Divina Commedia) is a poem written by Dante Alighieri in the period from 1307 to 1321 and gives the widest synthesis of medieval culture ... To use the preview of presentations, create a Google account (account) and sign in: https://accounts.google.com Slides captions:Circle The presentation was prepared by: Kislova Svetlana Igorevna Mathematics teacher MBOU secondary school No. 2 G. Lyskovo Goals and objectives: To systematize the theoretical material on the topic "Circumference". Improve problem solving skills. Prepare students for the test. To prepare students for the successful solution of the "Geometry" module when passing the OGE. tangent properties 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 B The square of the length of the tangent is equal to the product of the secant and its outer part. D C A B 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 Inscribed angle properties O A B D C B K A C Property of intersecting chords С В К А D Inscribed circle Each point of the bisector of a non-expanded angle is equidistant from its sides Inversely: each point lying inside the angle and equidistant from the sides of the angle lies on its bisector The sums of opposite sides are equal. Circumscribed circle Each point of the perpendicular bisector to the 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 Oral tasks on ready-made 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 C T O 70° ? Answer: 20° O Should be able to: Apply definitions, properties of figures, various theorems when solving problems. Be able to build a logical chain of reasoning. Apply the 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 C A Group 1 1 2 3 4 A C B D Group 3 1 2 3 4 C A AB C B On the topic: methodological developments, presentations and notesA math lesson in the 6th grade on the topic "Circumference. Circle. Circumference" is best done in the form of practical work .... The purpose of the lesson: to repeat the concept of a circle and a circle; calculation of the value of Pi; introduce the concept of the circumference of a circle and formulas for calculating the circumference of a circle .... The first lesson on the topic Circumference in grade 6. Practical work is being carried out, during which the guys calculate the value of the number pi. Getting to know Pi... Rodionova G. M. The number circle on the coordinate plane // Algebra and the beginning of analysis Grade 10//. The presentation contains material: the number circle on the coordinate plane, the main ... CIRCLE AND CIRCLE MATHEMATICS - 5 cells Goals and objectives of the lesson: Tutorials:
Developing:
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Equipment: interactive whiteboard, computer, drawing tools. The compass is a drawing tool. It has a needle on one end and a pencil on the other. The circle must be handled with care! 1. Mark a point in your notebook and mark it with the letter O. 2. Take a compass, 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. We got a closed line, which is called circle . What is a circle? Task number 1: Which figure 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 circle center . Circle - This is the simplest of the curved lines. One of the oldest geometric figures. Aristotle argued that the planets and stars should move along the most perfect line - the circle. For hundreds of years, astronomers believed that the planets move in a circle. Only in the 17th century, scientists: Copernicus, Galileo, Kepler, Newton refuted this opinion. Task 2 1) Draw a circle centered at O. 2) On the circle mark three points A, B and C. 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 on a circle are the same distance from the center. This distance is called the radius, denoted by - r . What is the radius of a circle? Circle radius is a line segment that connects the center of the circle and a point on the circle. Even the Babylonians and the ancient Indians considered the most important element of the circle - radius. The word is mathematical and means "beam". 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 "half-diameter". The term "radius" is first encountered in 1569 by the French scientist Rams. Generally accepted - "radius" becomes only in the 17th century. Euclid - Great Ancient Greek mathematician; first mathematician of Alexandria schools Construct two circles in a notebook with a radius of 2 cm. Paint over the inner area of one circle. Circle Circle How are the two drawings similar and how are they different? CIRCLE - a geometric figure consisting of all points of the plane that are inside the circle (including the circle itself). CIRCLE - a geometric figure consisting of all points located at the same distance from the center of the circle. Which objects are circle-shaped and which ones are circle-shaped? Task 3 Construct a circle centered 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 line segment that connects two points on a circle. Chord - this Greek word "chorde" - a string, was introduced by European scientists in the 12-13th centuries. A chord divides a circle into two arcs. CD = r+r = 2r = d = 2r "width="640" Task 4 Draw a chord through the center of the circle. This chord is called - diameter, denoted – d. Define diameter. Circle diameter is a chord passing through the center of the circle. CD = OC+OD, OC = r, OD = r = CD = r+r = 2r = d = 2r
d=2 r How are radius and diameter related? Extend line segment AO until it intersects the circle. Mark the point of intersection with the letter K. The segment AK is called diameter circles. Diameter denoted by the Latin letter d. Circle diameter is a line segment that connects two points on a circle and passes 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 that connects two points on a circle. Name all the radii, diameters and chords of a circle. Draw a circle centered at point O. Mark two points A and B on the circle. Points A and B divide the circle into two parts, which are called arcs circles. Formulate definition of arc circles. arc of a circle is the part of a circle enclosed between two of its points. Name all arcs on a circle: dots, lying on a circle. dots, not lying on a circle. dots, lying on a circle. Test Option 2 A1. What is the name of the 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 line 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 the 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 a line segment that... 1) connects any two points of the circle 2) connects the center of the circle to any point on the circle 3) connects two points of the 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. How far from the center of the circle are these points? The segments OM and OK are the radii of the circle, therefore OM=3cm, OK=3cm Solution Answer: at a distance of 3 cm Task number 1
How many points did you get? Solution Answer: two dots Task number 2
Solution Answer: none! Answer: one dot Task number 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 Summary of the lesson (reflection): Describe your impressions about today's lesson:
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