The tale of the triangle inequality. "Triangular Tale". Introducing middle group children to a plane figure - a triangle
Fairy tale "About an equilateral triangle."
Author Churinova Katya 6 “B” grade.
These fairy tales were invented by my 6th grade students as a final creative homework I know "
propaedeutics of geometry 6th grade." The school held KVN between the 6th grades of the same parallel and these fairy tales were chosen as the best homework assignments for dramatizations. The students approached creatively in preparing the geometry holiday.
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Tale "About Three Triangles".
Once upon a time there were three brothers of a triangle: the eldest was rectangular, the middle one was acute, and the youngest was obtuse. And the brothers decided to go to the city for the fair.
At that time, King Tetrahedron proclaimed that whoever solved the problem would give his only daughter, the beautiful Pyramid Correct, as his wife. Odes were written about the beauty of the Pyramid. And more than once brave souls came from all over the world to try to solve the king’s problem.
And the brothers decided to try their luck. They came to the palace and learned that whoever did not solve the problem would be executed. Rectangular and Acute Angular got scared and decided to leave. And Obtuse fell in love with the Pyramid so much that he decided to try.
The king set the task:
The area of the palace garden is 27.3 m 2 , the area of the palace is 4.8 m 2 less than the garden, and the area of the city is 1.6 times more area palace What is the area of the three plots together?
Tupugolny proposed the following solution:
- 27.3 – 4.8 = 22.5 (m2)
- 22.5 * 1.6 = 36 (m2)
- 27.3 + 22.5 + 36 = 85.5 (m2)
The decision turned out to be correct. King Tetrahedron gave his daughter in marriage. And the young people lived happily ever after.
Fairy tale "About an equilateral triangle."
In a certain kingdom, in a certain state, far away, in the thirtieth state, there lived a strong, mighty, beautiful fellow, the Equilateral Triangle. The best of all triangles, handsome, all sides are the same. Somehow he wanted to see the world and show himself. He took with him his close friend Rectangular Triangle.
They walked past a geometric pond, through a forest of bisectors, through foggy planes. Suddenly they see: a huge, menacing Rectangle is sitting in the middle of the road, blocking the entire road with itself - it is impossible to pass or pass.
The rectangle tells them:
And the Triangle friends answered without hesitation:
This is the perimeter!
The rectangle got angry; he had never met such smart travelers. And out of anger he split into two squares, which still lie on the sides of the road. Let's move on, friends. After some time they heard a call for help. Tall Oval asked to help him remember the definition of length.
I used to be very round, but somehow I fell and stretched out.
Friends triangles did not leave him in trouble, and the Oval returned to the shape of a circle again. And they took him with them. Further and further they drove and found themselves at the very edge of the world, where the red sun rises. Suddenly they see a beautiful palace made of sparkling parallelepipeds. The ruler of the palace was the wise Gradus, and he had a beautiful daughter, Bisector.
Attention! Attention! Attention! The Great Degree announced a tournament. The winner of the tournament will receive the beautiful Bisector as a wife and half a kingdom to boot!
Equilateral Triangle decided to try his hand at this tournament. Many participants came, but no one could guess the three riddles of Degree. And only the Equilateral Triangle was able to answer.
First riddle: How to find the area of a rectangle?
The area of a rectangle is equal to the product of its adjacent sides.
Second riddle: Not a single geometric figure can do without this. It has a unit of measurement the same as temperature and consists of four letters, the first of which is also a preposition, and the other three are what can cause joy or sadness in the fans.
And again, Equilateral Triangle was the only one who could answer correctly.
It's a corner!
Third riddle: What is five times five?
Everyone shouted different answers: 24, 26, and even 0! But again, the correct answer was given by the Equilateral Triangle:
The product will be equal to 25!
The Equilateral Triangle received the beautiful Bisector and half of the kingdom as his wife. And they lived happily ever after.
Fairy tale "Terrible Letter".
Once upon a time there were two Squares. One day they were sitting at home. And suddenly someone knocked on the door. The First Square ran to open it. It turned out to be Krug with a letter. Kvadrat ran joyfully into the room with a letter in his hands.
Maybe it's about our Friend! - said the second Square and began to make out the address on the envelope, which was written in illegible scribbles.
The entire envelope was covered with stamps and stickers with inscriptions.
This is not a letter to us,” the first Square finally said. This is for our dad Rectangle. Some very literate Oval wrote. I made two mistakes in one word: instead of “Sandy Street,” I wrote “Pechnaya Street.” Apparently, the letter traveled around the city for a long time until it reached the right place...
Daddy Rectangle! - shouted the second square. You have a letter from some oval literate person!
What kind of oval letter is this?!
But read the letter.
Papa Rectangle tore the envelope and began to read in a low voice:
- “Dear daddy Rectangle! Let me keep the little puppy Rombik. He is very handsome, all red, and his ear is black, and I love him very much...”
What is this? - asks dad Rectangle, - you wrote it!
The first square laughed and looked at brother Kvadrat. The second square turned red like boiled crayfish and ran away.
***
Once upon a time there were two brothers:
Triangle with Square.
The eldest is square,
Good-natured, pleasant.
The youngest is triangular,
Always dissatisfied.
He began to ask Kvadrat:
“Why are you angry, brother?”
He shouts to him: “Look:
You are fuller and wider than me.
I only have three corners
You have four of them.”
But Square replied: “Brother!
I’m older, I’m a square.”
And he said even more tenderly:
“It’s unknown who is more needed!”
But night came, and to my brother,
Bumping into tables
The younger one climbs stealthily
Cut corners for the elder.
As he left, he said: “Have a nice
I wish you dreams!
When I went to bed I was square,
And you’ll wake up without corners!”
But the next morning little brother
I was not happy about the terrible revenge.
He looked - there was no square.
I was speechless... I stood there without words...
So much for revenge! Now my brother
Eight brand new corners!
The Tale of Triangles
Once upon a time there lived an important geometric figure. Its importance was recognized by all people, for in the manufacture of many things its form served as a model. Favorite song of this miracle figure
Every schoolchild knows me
And I'm called a triangle.
I have three peaks,
Also three and sides.
My two angles at the base are equal and the sides are the same, the triangle thought and decided to call itself isosceles.
The isosceles triangle was bored alone, so he went to look for friends. Somehow he comes across a figure: three sides and three angles. There's only one right angle! Hooray! This right triangle! They began to be friends.
Work together, have fun together. Somehow we came across a segment and decided to experiment: we attached it with one end to the top and the other to the middle opposite side. Beauty, it will be MEDIAN! Let's try again - divide the angle in half!
Everything also jumps around the corners
Cheerful, funny rat.
We share the joy in half,
And the bisector divides the angle.
This is how they spent their leisure time. One day, while walking through the forest, we met a very similar couple. We met and started playing comparison. An isosceles triangle was pressed against a triangle similar to itself and all the points coincided. Hooray! We are the same. They thought about equality and came up with three theorems:
-if two sides and the angle between them of one triangle are respectively equal to two sides and the angle between them of another triangle, then the triangles are congruent;
- if a side and two adjacent angles of one triangle are equal, respectively, to a side and two adjacent angles of another triangle, then the triangles are congruent;
- if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.
Friends spend a lot of time together and meet new ones.
Plum Pit.
As it should be, in a fairy tale we begin with the vein. So, there lived a Plum Pit. Once upon a time she was thrown into a box desk and have since been forgotten. Plum Pit quickly became acquainted with her neighbors: pens, pencils, notebooks. These were all important and brilliant people! They constantly talked about their need and importance. Everyone, without exception, even the eraser, looked down on Plum Pit and often reproached her for being completely useless. Therefore, she had to occupy the farthest and darkest corner of the box.
Sometimes a box would be pulled out and someone would disappear for a long time. Residents returned quiet and in a deplorable state: notebooks crumpled, covered with writing, and sometimes simply torn, pencils and pens broken and even bitten. They no longer boasted, but they never talked about their adventures either. Many disappeared completely.
And when there was not a single brilliant person left in the box, they stopped opening it altogether. The Plum Pit has dried up and become covered with dust. It seemed to her that she was about to die, her strength was leaving her. The box was pulled out of the table and everyone was thrown into the trash container, and the Plum Pit fell past and no one even noticed.
Rain is coming. A stream of water picked up Plum Pit, trembling with fear, and carried it to an abandoned wasteland overgrown with burdocks and nettles. A huge number of ants immediately surrounded the guest. And they dragged me into an underground anthill. Well, that’s all, Plum Pit thought, when she suddenly felt strength and a surge of energy. She straightened up and a small green sprout appeared on the surface. The sprout reached towards the sun, growing by leaps and bounds. And Plum Pit didn’t even notice how she turned into a beautiful slender flowering miracle tree. By autumn the fruits had ripened, there were so many of them that there was enough for both the local children who came running to the vacant lot to play, and the adults who came to look at the miracle tree. And many fruits simply fell to the ground...
How much time has passed, but that wasteland has turned into a beautiful garden. And maybe more than one daughter or granddaughter of Plum Pit will repeat her path!
Once upon a time in this world there lived a King Compass and a Queen Ruler. They had a large kingdom in which lived points, segments, squares, triangles and many other different shapes.
And not far from the palace lived a family - three brothers. Three isosceles triangles - the eldest is rectangular, the middle is acute, and the youngest is obtuse. They were lazy and always had nothing to do. And out of boredom, they decided to argue about which of them was better.
- I have the largest sum of angles! - said the obtuse one. - what a big corner I have!
- No, my sum of angles is greater! - objected the rectangular one.
- But I can change my shape! - shouted the sharp-angled one.
“Let’s all go to the old man Protractor,” suggested the rectangular one. - He is wise, he will judge us all.
The triangles walked for three days to the Diamond-shaped Protractor Mountain. On the first day they made their way through the jungle of segments and rays. On the second day they swam across lakes Krugloye and Ovalnoye. On the third day they walked through square gorges. And finally we reached the mountain. They climbed the mountain and approached the Protractor.
“Wise Protractor, judge us,” said the rectangular one. - We had an argument about who is better.
- Okay, I'll help you. Say what you need.
And the triangles began to murmur vyingly:
- Measure all the angles for me! Not for me! And me! Only, mind you, I'm first!
- Stop. Hush hush. You don't need to measure all the angles. You are equally bad! You only need to measure one corner for each. Here you are, stupid, come here.
The younger one stuck his tongue out at the brothers and approached the old man.
The old man measured one corner for him and said:
- Two of you are 40 degrees each, and one is equal to one hundred degrees. – the old man did the same with his middle brother. “And you,” he turned to the rectangular one, “don’t need to be measured at all.” Two for forty-five and one for ninety.
- Wow. Who has the greater sum of angles?
- Just wait! – the elder interrupted the younger. - How did you calculate it so quickly?
- Yes, everything is easy here. The sum of the angles is the same for everyone
The corners looked at each other and smiled.
- Wise Protractor, tell them that I can change shape as I want! – the sharp-angled one remembered.
- No, I will change as I want!
- No, I!!!
- You are all mistaken, the remarkable thing about triangles is that they cannot change. Live as you were born. – Protractor explained everything.
- Well, so what, but I’m the most important! - said the obtuse one.
- No, I am more important.
- I'm the best!!!
- You are all important. Here, you, rectangular, are used when they build pyramids in honor of the king. And you, sharp-angled one, help us defend the kingdom, because you are the tip of spears and arrows. And you, stupid one, make the little kids happy, because you are the one who plays the role of slides on playgrounds. - the old man reconciled the brothers.
- Thank you, Protractor, you showed us that we are all important. Now we are friends.
The brothers went to their place. And he lived there in chocolate and super-duper-happily.
The triangles thought for a long, long time about what the Goddess said and why she gave the hoop, and they decided to organize a competition “The most beautiful figure.” The competition included obtuse, acute, rectangular, isosceles, equilateral and scalene triangles. The first task was this: each triangle must touch a circle so that the circle is circumscribed and the triangle is inscribed. At first they didn't succeed:
Bisectors. The second task was this: place a circle inside yourself so that the sides touch the circle (an inscribed circle, and a circumscribed triangle). It didn't work out at first either. And then their maids, Bisectors, helped them. Everyone did a great job.
But no one was offended as much as everyone felt beautiful and happy. And they began to choose a king and queen. At first they chose an equilateral triangle as queen, but she turned out to be a minor, and therefore her mother, an isosceles triangle, was chosen. And the king is a right triangle.
