entranceLabel each polygon, measure the lengths of the sides of each. Quadrilateral
In this lesson, we will learn what a polygon is. We will also get acquainted with a new shape - a quadrangle, consider its elements (vertices, sides, corners). We will also learn how to recognize a quadrilateral among other polygons in the figure and give it a mathematical name. Studying this topic will allow you to solve geometric problems with ease in the future.
Theme:Familiarity with basic concepts
Lesson: Quadrilateral. Quadrangle notation
Polygon is a figure with several vertices, several sides, several angles.
Exercise 1... Divide given in Fig. 1 polygons in two groups.
Solution:
The first group is a group of triangles (Fig. 2).
Triangles are shapes with 3 corners, 3 vertices and 3 sides.
The second group is a group of polygons (Fig. 3). To determine their names, you need to count the number of corners, sides and vertices.
So, a shape with 4 sides, 4 corners and 4 vertices is quadrangle .
Each polygon can be assigned a mathematical name using Latin letters. Some of them are shown in Fig. 4.
In order to name a quadrangle, it is enough to put one letter at each of its vertices.
Example 1: Give a name to the polygon.
Putting a Latin letter at each of the vertices of the polygon, we got quadrangleABCD.
Answer: QuadrangleABCD
So, in this lesson we looked at polygons such as triangles and quadrangles. It also studied how to name the quadrangles using Latin letters.
Bibliography
- Alexandrova L.A., Mordkovich A.G. Grade 1 mathematics. - M: Mnemosina, 2012.
- Bashmakov M.I., Nefedova M.G. Maths. 1 class. - M: Astrel, 2012.
- Bedenko M.V. Maths. 1 class. - M7: Russian Word, 2012.
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On this page you will find examples and problems with detailed solutions from a workbook on mathematics for grade 2 under the program Perspective authors: Dorofeev G.V., Mirakova T.N. Buka T.B. for the 2018 - 2019 academic year.
Select the problem you need from the list and see the solution or go to the page with the solution.
Topic: Addition and Subtraction (Repetition)
Page 4 (# 1)
Fill in the blanks with numbers as shown in the sample.
Page 4 (# 2)
Draw a path from the duck to the lake so that houses are located to the left of it, whose number on the roof is less than the number in the window by 9, and to the right by 8. 
Page 4 (no. 3)
Perform calculations. Decipher the word for the tallest mountains on Earth by writing down the answers of the examples in ascending order.
Page 4 (No. 4)
Put a + or - in a circle to get the correct entry.
Page 5 (No. 5)
Build and solve circular examples.
Page 5 (No. 6)
On the table are a blue teapot, a green vase and a red cup. Color them so that in the left picture the cup is in front of the teapot, and the vase is behind it, and in the right picture there is a teapot in front and a cup behind the vase. 
Solution 
Page 5 (№7) (problem about two snails)
To see the solution follow the link: No. 7 (problem about two snails)
Page 6 (# 1)
Three boys - Vitya, Gleb and Misha - photograph the playground from different sides. Which of the boys took this photo? 
Answer: Gleb took the photo.
Page 6 (# 2)
Compare.
Solution:
Page 6 (no. 3)
Perform calculations. Decipher the name of the geometric shape by writing down the answers of the examples in decreasing order. 
Solution:
First, let's do the calculations: 
Let's arrange the received answers in decreasing order. We get the following sequence of numbers: 17, 16, 14, 13, 12, 11, 10, 9, 8, 7, 5, 4, 3, 2, 1
Substitute the corresponding letters and get the word: FOUR CORNER.
Page 6 (No. 4)
Fill in the blanks with numbers to get the correct entries.
Solution:
Page 7 (# 5)
Complete the schemes and solve the problems.
1. 8 large nails were used to repair the bench, and 3 more small nails than large ones. How many big and small nails went to repair the bench? 
Solution:
First, let's fill in the diagram: 
1) 8 + 3 = 11 (g.)
2) 8 + 11 = 19 (g.)
Answer: 10 nails.
2. One car had 7 seats, and the other had 2 fewer seats. How many seats were there in these two cars?
1) 7-2 = 5 (m.)
2) 7 + 5 = 12 (m.)
Answer: 12 places.
Page 7 (No. 6)
Measure in centimeters the length of each segment and record the results.
Solution:
AB = 7 cm, SD = 4 cm, ME = 3 cm.
Page 7 (No. 7)
SO and NOT IT made up words from the box of letters. THAT made four words correctly, and NOTAC rearranged the letters in them. Try to read these words. Find and cross out the unnecessary word:
- RETRACTING
- RAMPYA
- ZETROKO
First, let's decipher the words:
- POINT - POINT
- RAMP - STRAIGHT
- TIRL - LITER
- ZETROKO - INTERCEPT
The word “liter” will be superfluous in this list, since this is a unit of measurement, and the rest of the words are the simplest geometric shapes.
Directions and beams
Page 8 - 9
1. Show with an arrow, as in the sample, in which direction you need to send the white ball so that it, without hitting the edge of the billiard table, knocks into the pocket: a) blue ball, b) red ball, c) yellow ball, d) brown ball ...
Let's draw arrows indicating the direction of the white ball in order to knock out each of the balls with the corresponding colors.
2. Draw the direction of the wind in each drawing with an arrow.
3. Fill in the blanks with numbers as shown in the sample.
4. Draw on that figure, where possible, with a red pencil, a ray starting at point A so that it intersects all rays emanating from point B.
In the figure on the left, you can draw a ray with the beginning at point A so that it intersects all the rays that come out of point B.
5. Complete the schemes and solve the problems.
1) There were 6 gingerbread on one plate, and 5 on the other. Sasha took 8 gingerbread. How many gingerbread cookies are left on the plates?
6. Place a + or - in a circle to get the correct entry.
Solution: 15 - 5 = 10 8 + 6 - 3 = 11 14 - 6< 10 15 + 5 = 20 8 + 6 + 3 = 17 14 + 6 > 10
Page 10 - 11
1. Perform calculations. Decipher a mathematical term by writing down the answers of the examples in ascending order.
Let's perform the calculations and write down the answers in ascending order.
Let's get a mathematical term - direction.
Answer: The coded mathematical term is direction.
2. Mark points A, B and C in the notebook as shown in the drawing. Draw a ray with a beginning at point A with a red pencil, and a ray with a beginning at point B with a green pencil so that point C turns out: a) on a red ray, but outside the green ray; b) on red and green rays.
3. Restore the records.
Solution: 11 - 1 - 5 = 5 12 - 2 - 2 = 8 13 - 3 + 1 = 11 14 - 4 - 4 = 6 15 - 5 - 1 = 9 16 - 6 + 2 = 12 17 - 7 - 3 = 7 18 - 8 - 0 = 10 19 - 15 + 9 = 13
4. A cow is 7 years old, a sheep is 4 years old, and a ram is 9 years younger than a cow and a sheep together. How old is the ram?
Solution: 1) 7 + 4 = 11 (l.) 2) 11 - 9 = 2 (year) Answer: the ram is 2 years old.
5. Take measurements. Fill in the blanks with the results obtained. Find and draw with a red pencil the shortest path leading from point A to point B.
Solution: 
2 + 3 + 1 + 5 = 11 (cm) Answer: the length of the shortest path from A to B is 11 cm.
6. Determine by what rule the pattern is made. Continue it.
Solution: Let's continue the pattern and get
Number beam
Page 12 - 13
1. Numbers are marked on the ray in the order they go when counting. Fill in the blanks.
2. A grasshopper in a blue jacket jumped 3 spaces to the left along the number beam, and a grasshopper in a red jacket jumped 9 spaces to the right. Mark the points of the number ray where the grasshoppers will find themselves in red and blue, respectively. Has the distance between the grasshoppers changed and by how many divisions?
Between the grasshoppers there was 5 divisions. Between the grasshoppers became 7 divisions. Distance changed to 2 division.
3. Find the sail for each boat so that the answer to the example on the boat is equal to the number on the sail. For the remaining sail, draw a boat and write an example on it.
4. The weight of the box with apples is 12 kg, and with plums it is 5 kg less. Find the mass of the box of plums.
Solution: 12 - 5 = 7 (kg) Answer: the weight of the box with plums is 7 kg.
5. Fill in the blanks in the tables by performing the calculations.
6.on each drawing?
7. Three brothers - Vanya, Sasha and Kolya - study in different classes of the same school. Vanya is younger than Kolya and older than Sasha. Write the name of the oldest brother, middle and youngest.
Solution: Note on the number line the age of the brothers. Since Vanya is younger than Kolya, then on the number line he will be marked to the left. The problem statement also says that Vanya is older than Sasha, that is, on the number line he will be marked to the right of Sasha. As a result, we get the following straight line. 
The elder brother's name is Kolya, the middle one is Vanya, the younger one is Sasha.
8. Numbers from 4 to 9 are written in a row. Try to put a + sign between them
or - so that the result is 7.
Solution: 4 + 5 + 6 - 7 + 8 - 9 = 7
Page 14 - 15
1. The squirrel and the hare are jumping along the number beam. First the squirrel jumps, and then the hare. Each jump of a squirrel is equal to 3 divisions, and a hare - 6 divisions. At what point will each of them be after 3 jumps? Mark these points on the finishing ray with the letters B and Z, respectively.
From the figure we see that after 3 steps the Squirrel will be at point 9, and the hare at point 18. Answer: the squirrel will be at point 9, and the hare at point 18. 2. For each picture, compose two examples for adding the same numbers. Solve these examples.
3. Fill in the blanks with numbers to make the correct entries.
1) Pasha had 18 rubles. He bought the album for 9 rubles. and a pen for 5 p. How much money does Pasha have left?
2) There were 16 liters of milk in the can. First, they took 7 liters of milk from it, and then another 4 liters. How many liters of milk are left in the can?
3) A piece 5 cm long was cut from a bar of butter 14 cm long, and a piece 2 cm long at the other end was cut off. Determine the length of the remaining piece of butter.
5. Three classmates - Sonya, Tanya and Vera - are engaged in various sports sections: one in gymnastics, the other in skiing, and the third in the swimming section. What kind of sport does each of them do, if it is known that Sonya is not interested in swimming, and Vera is the winner in skiing competitions?
Solution: The problem statement says that faith- the winner in the skiing competition, it means she is engaged in the ski section... It is also said in the problem statement that Sonya is not fond of swimming, and she also does not practice in the ski section, which means she walks in the gymnastics section... And by the method of elimination we get that Tanya attends swimming section... Answer: Vera is in the ski section, Sonya is in the gymnastics section, and Tanya is engaged in swimming.
Page 16 - 17 - Beam Designation
1. Write down the designations of all the rays in the drawing.
Answer: the drawing indicates the rays: AB, VU, BE, VD, IK, OG.
2. Perform calculations. Decipher the name of the fairytale hero by writing down the answers of the examples in decreasing order.
Answer: the name of the fairytale hero Prospero from the work "Three Fat Men" by Yuri Olesh.
3. Complete short notes and solve problems.
1) During the summer holidays, Vitya painted 4 portraits, 6 still lifes and 8 landscapes. How many pictures did Vitya paint during the summer holidays?
4. Fill in the gaps on the bows as shown in the sample.
5. How many triangles and how many quadrangles are there in the star shown in the picture?
 |
Triangles - 8 Quadrilaterals - 5 |
 |
|
 |
|
6. Which of the numbered figures on the right is missing from the table? Circle her number. Draw this shape in an empty cell on the table.
Page 18 - 19 - Corner
1. Mark with an arc in the drawing all the corners of the quadrilateral and triangle, as shown in the sample. Fill in the blanks in the proposals.
Solution: 
There are only 4 corners in a quadrilateral. There are only 3 corners in a triangle.
2. Nadya is 12 years old, and her sister is 6 years younger. How old is your sister?
Solution: 12 - 6 = 6 (l.) Answer: sister is 6 years old.
3. Complete the diagram and solve the problem. Try to find two solutions.
The boy had 15 rubles. He bought a bun for 9 rubles and tea for 3 rubles. How much money does the boy have left?
4. Fill in the blanks in the tables by performing the calculations.
5. Fill in the blanks as shown in the sample.
6. Decipher the words. Cross out the extra word.
| RGUK | UCHL | GUOL | ISLOCH |
| CIRCLE | RAY | INJECTION | NUMBER |
Page 20 - 21 - Angle designation
1. On each dial, mark with an arc the angle between the hands of the watch, as shown in the sample.
2. Write a label for each corner.
The figures show the angles EGM, DAB and KVU.
3. Draw the corners ABC and DEC using these points.
4. Fill in the blanks with numbers to get the correct entries.
Solution: 1 dm 2 cm = 12 cm 14 cm = 1 dm 4 cm 1 dm 5 cm = 15 cm 17 cm = 1 dm 7 cm 2 dm 1 cm = 21 cm 11 cm = 1 dm 1 cm
5. Solve the examples and find out with what score the water polo match between the teams "Seals" and "Walruses" ended. It is known that balls were scored into the Seals 'goal, the answers of examples to which are less than 15, and all other balls were scored into the Walruses' goal. Record the score of the match.
6. On the table are a blue square, a red triangle and a yellow circle cut out of colored paper. Color the shapes so that: a) the triangle is on top, there is a square under it, and the circle is at the very bottom; b) the pieces were in reverse order.
Page 22 - 23 - The sum of the same terms
1. Check the box, as shown in the sample, only the sums of the same terms. Solve these examples.
2. Write on the right, as shown in the sample, an example for the addition of identical terms, in which you need:
1) take 2 3 times: 2 + 2 + 2 = 6 2) take 3 4 times: 3 + 3 + 3 + 3 = 12 3) take 1 8 times: 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 8
Solve these examples.
3. Counting from 1 to 20, mark every third number and paint a ball with this number on the drawing.
4. Find out from the picture the weight of each bag of flour.
 |
 |
| Solution: 1) 10 + 3 = 13 (kg) 2) 13 - 5 = 8 (kg) Answer: the weight of the bag is 8 kg. |
Solution: 1) 15 - 3 = 12 (kg) 2) 12 - 3 = 9 (kg) Answer: the weight of the bag is 9 kg. |
5. Compare.
Solution: 2cm + 9cm< 12 см 14 см - 1 дм = 4 см 6 см + 7 см >11 cm 18 dm - 8 dm = 10 cm 8 cm + 8 cm< 2 дм 15 см - 4 см >1 dm
6. Teddy bear hurries home. Help him find the shortest road - the example answer on it will be less than on the other two roads. This will be the house number of the bear.
Write the resulting number in the empty box. Color the figures on the found road with one color.
Page 24 - 25 - Multiplication
1. Link the example to his answer. Check the box for the sum of the same terms as shown in the sample.
2. Write down examples using the multiplication sign. Solve them.
3 + 3 + 3 + 3 + 3 + 3 = 3 * 6 = 18 2 + 2 + 2 + 2 + 2 + 2 + 2 = 2 * 7 = 14 4 + 4 + 4 = 4 * 3 = 12 5 + 5 + 5 = 5 * 3 = 15 7 + 7 = 7 * 2 = 14
3. There were 3 squirrels. Each squirrel was given 2 nuts. How many nuts were given to all the squirrels? Draw nuts for each squirrel. Fill in the blanks in the proposal.
Solution: 
Take 2 3 times, you get 6.
4. Guess how the numbers in squares and circles are related. Fill in the blanks.
5. On one tree there were 12 crows, and on the other - 7 fewer crows. How many crows were there in the two trees?
6  |
Solution: 1) 12 - 7 = 5 (c.) 2) 5 + 12 = 17 (c.) Answer: on two trees there were 17 crows. |
6. On the dotted line, draw a segment OK, which is 2 cm longer than this segment AB.
7. Draw a green pencil path along which the puppy needs to run in order to overcome obstacles to get to the bone.
Page 26 - 27
1. Draw 3 patties on each plate. How many pies did you get? Fill in the blanks in the example and in the sentence.
Solution: 3 * 5 = 15 Take 3 5 times, you get 15.
2. Find an anchor for each boat.
3. Fill in the blanks in the tables by performing the calculations. 
4. One can contains 3 liters of honey. How many liters of honey are there in 4 such jars?
5. Fill in the blanks with numbers to get the correct entries.
1 dm 3 cm = 13 cm 15 cm = 1 dm 5 cm 1 dm 6 cm = 16 cm 18 cm = 1 dm 8 cm 2 dm 7 cm = 17 cm 10 cm = 1 dm
6. Create and solve circular examples.
7. How many triangles and how many quadrangles do you see in the drawing?
Answer: in the drawing there are 4 triangles and 6 quadrangles.
8. Foma and Erema divided 7 rubles among themselves, and Foma received 3 rubles more than Erema. How much money did everyone get: Write an answer.
Solution: 1) 7 - 3 = 4 (p.) 2) 4: 2 = 2 (p.) 3) 2 + 3 = 5 (p.) Answer: Foma got 5 rubles, and Eryoma got 2 rubles.
Page 28 - 29 - Multiplying the number 2
1. Draw 2 carrots for each bunny. How many carrots are there in total? Fill in the gaps in the entry.
Solution: 
2 + 2 + 2 = 2 * 3 = 6 (m.)
2. Draw 2 circles on each wing of the butterflies. How many circles did you get?
Solution: 
2 + 2 + 2 + 2 + 2 + 2 = 2 * 6 = 12 (c.)
3. Connect each body to the cab so that the sentence and the example mean the same thing.
4. Complete the schemes and solve the problems.
1) 7 people dined at one table, and 3 fewer at the other. How many people dined at two tables in total?
 |
Solution: 1) 7 - 3 = 4 (h.) 2) 7 + 4 = 11 (h.) Answer: 11 people dined at two tables. |
2) 11 people dined in the dining room. Then 6 more people came, and 2 people left. How many people are left in the dining room?
5. From the figures numbered on the right, collect the "cat" that is missing in the table. Circle the numbers of the shapes you want. Draw a "cat" in an empty cell on the table.
Page 30 - 31
1. In each rectangle, draw and color 2 circles. How many circles are drawn in total?
Solution: 2 + 2 + 2 + 2 + 2 = 2 * 5 = 10 (c.)
2. One package contains 2 kg of noodles. How many kilograms of noodles are there in 7 such bags?
Solution: 2 + 2 + 2 + 2 + 2 + 2 + 2 = 2 * 7 = 14 (kg.) Answer: there are 14 kg of noodles in 7 bags.
3. At the numerical centipede, the shoes of each pair are numbered so that if you multiply these numbers, you get the number on the corresponding shirt. Write down the missing numbers.
4. For each example, find the answer and connect the strips, taking into account the break line.
5. Compare.
3 l< 13 л 2 см = 20 дм 20 см = 2 дм 16 кг >10 kg 1 dm = 10 cm 2 dm> 16 cm
6. The ball costs 12 rubles, the doll is 5 rubles more expensive than the ball, and the notebook is 9 rubles cheaper than the ball. How much does a doll cost and how much does a notebook cost? Write down the answers.
Solution: 12 + 5 = 17 (p.) 12 - 9 = 3 (p.) Answer: a doll costs 17 rubles, a notebook costs 3 rubles.
7. Measure the lengths of the segments and record the results.
MB = 5 cm BC = 2 cm TA = 7 cm EI = 4 cm
8. How many digits will it take to number the 14 figures in the album, starting with number 1?
Solution: Let's write down the numbers of the figures in order: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 There are 9 single-digit and 5 two-digit numbers in the recorded sequence. Let's count the number of digits used: 5 * 2 = 10 (c.) 10 + 9 = 19 (c.) Answer: to number 14 figures in the album, you need 19 digits.Broken line. Polyline designation.
Page 31 - 32
1. Find the broken lines on the picture and circle the closed broken lines in blue, and the open ones in red.
2. In each frame, draw a broken line ABOKM with a green pencil so that a closed broken line appears in the frame on the left, and an open one on the right.
Closed (left) and open (right) polygonal lines 3. Perform calculations. Decipher the name of mathematics by writing down the answers of the examples in ascending order.
Answer: the name of the mathematical science is logic.
4. Draw 3 paths along which Fedya can get to school: a) by bus; b) by bike; c) on foot.
5. Masha has 6 coins, 2 rubles each. each, and another 5 p. How many rubles does Masha have? Fill in the blanks.
1) 2 * 6 = 12 (p.) 2) 12 + 5 = 17 (p.) Can Masha buy ice cream for 9 rubles with this money? and lollipops for 6 rubles.
1) 9 + 6 = 15 (p.) 2) 17> 15
Check the box for the correct answer.
Answer: Yes, Masha can use her own money to buy ice cream for 9 rubles and candy canes for 6 rubles.
Page 34 - 35
1. In this drawing, outline all the polygons with a red pencil.
2. Draw an ABSDE polygon from these points. Mark with arcs its corners SDE and AED.
3. Solve the examples using the number ray as shown in the sample.
Solution:
4. Complete the schemes and solve the problems.
1) My grandmother has 7 geese and 15 chickens in the village. How many fewer geese are there than chickens?
5. Place the + or - signs in the circles so that you get the correct entries.
Solution: 13 + 2 - 8 = 7 7 + 5 + 4 = 16 6 + 10 - 3 = 13 9 - 8 + 11 = 12
6. Compare.
Solution: 1 dm 2 cm - 7 cm< 6 см 15 см - 1 дм >4 cm 1 dm 4 cm + 5 cm< 2 дм 11 см + 3 см < 1 дм
7. Fill in the gaps by performing the calculations.
Multiplication of the number 3
Page 36 - 37
1. Draw 3 seeds for each chicken. How many grains did you get? Fill in the blanks.
Solution: 3 + 3 + 3 + 3 + 3 = 3 * 5 = 15 (h.)
2. Designate the vertices of each polygon with letters on the drawing.
How many letters did you need? Write it down.
Solution: 
To designate polygons, 9 letters were needed: A, B, C, O, M, P, T, E, X.
3. Draw an open polyline ABSDE based on these points.
Measure the length of each link and calculate the total.
Solution: 
AB + BS + SD + DE =
4. Check if the given examples are circular. If so, connect them with a line so that the answer from the previous example is the first number in the next example.
5) Complete the diagram and solve the problem. One set has 12 cups, and the other has 6 fewer cups. How many cups are there in two sets.
 |
Solution: 1) 12 - 6 = 6 (h.) 2) 12 + 6 = 18 (h.) Answer: there are 18 cups in two sets. |
6. The family has three children: two boys and a girl. Their names begin with the letters A, B, G. Among the letters A and B there is the initial letter of the name of only one boy. Among C and D there is only the initial letter of the name of the other boy. What letter does the girl's name begin with?
Solution: The problem statement says that among the letters A and B there is an initial letter of the name only one boyToa , then the second letter from A and B is the initial letter of the girl's name. By the elimination method, we obtain that second brother's name - starts with the letter Г ... Also in the condition of the problem it is said that among C and D there is an initial letter of the name just another boy .Since we found out that the name of the second boy begins with the letter G, then the girl's name begins with the letter B ... Respectively with letter And the name of the first brother begins ... Answer: the name of the first brother is called with the letter "A", the name of the second brother begins with the letter "G", the name of the girl begins with the letter "B".
Page 38 - 39
1. Draw and color 3 cucumbers on each plate. How many cucumbers are drawn in total?
3 + 3 + 3 + 3 = 12 cucumbers.
2. One can contains 3 kg of paint. How many kilograms of paint are in 6 such cans?
3 + 3 + 3 + 3 + 3 + 3 = 3 * 6 = 18 kg.
3. Connect each suitcase to its handle so that the sentence and the example mean the same thing.
4. Compare.
2 * 2 = 2 + 2 3 * 3 > 3 + 3 2 * 5 > 2 + 5 2 * 3 > 2 + 3 3 * 4 > 3 + 4 3 * 6 > 3 + 6 2 * 4 > 2 + 4 3 * 5 > 3 + 5 2 * 8 > 2 + 8
5. Who will be the first to score a goal in the match between the teams "Squares" and "Triangles"? The rules are as follows: a football player can only pass the ball to the player whose shirt number is equal to the answer of the example written under the given football player. For example, player number 7 will pass the ball to player number 6, since 2 * 3 = 6. Draw a smooth line for the transfer of the ball from player to player. Kick the ball into the goal.
The ball was scored by a player of the team “Triangles! at number 3.
6. Compare.
14 kg> 4 kg 12 cm> 1 dm 1 dm 3 cm< 2 дм 18 л >10 l 2 dm> 10 cm 1 dm 7 cm = 17 cm
7. Lyuba is 11 years old, Nadia is 4 years younger than Lyuba, and Vera is 7 years older than Nadia. How old is Nadya and how old is Vera? Write down the answers.
Nadya is 11 - 4 = 7 years old. Vera 7 + 7 = 14 years old.
Page 40 - 41
1. Fill in the blanks in the tables.
2. Solve the examples using the number ray.
3. Perform calculations. Decipher the name of the heroine of the fairy tale by arranging the answers of the examples in ascending order.
Polygon is a geometric figure bounded by a closed polyline that does not have self-intersections.
The links of the broken line are called sides of the polygon, and its tops are the vertices of the polygon.
Corners polygon are called interior corners formed by adjacent sides. The number of corners of a polygon is equal to the number of its vertices and sides.
Polygons are named according to the number of sides. The polygon with the least number of sides is called a triangle, it has only three sides. A polygon with four sides is called a quadrangle, a polygon with five is called a pentagon, and so on.
The designation of a polygon is made up of the letters at its vertices, naming them in order (clockwise or counterclockwise). For example, they say or write: pentagon ABCDE :
In the pentagon ABCDE points A, B, C, D and E are the vertices of the pentagon, and the segments AB, BC, CD, DE and EA- the sides of the pentagon.
Convex and concave
The polygon is called convex if none of its sides, continued to a straight line, intersects it. Otherwise, the polygon is called concave:
Perimeter
The sum of the lengths of all sides of the polygon is called it perimeter.
Polygon perimeter ABCDE is equal to:
AB + BC+ CD + DE + EA
If a polygon has equal all sides and all angles, then it is called correct... Only convex polygons can be regular polygons.
Diagonal
Polygon diagonal is a line segment connecting the vertices of two corners that do not have a common side. For example, the segment AD is the diagonal:
The only polygon that does not have any diagonal is a triangle, since it has no corners that have no common sides.
If all possible diagonals are drawn from any vertex of the polygon, then they will divide the polygon into triangles:
There will be exactly two less triangles than sides:
t = n - 2
where t is the number of triangles, and n- the number of parties.
Dividing a polygon into triangles using diagonals is used to find the area of a polygon, since to find the area of some polygon, you need to split it into triangles, find the area of these triangles and add the results obtained.