What are the eight axioms of junior high school mathematics?

Mathematical theorem

The complementary angles of the same angle (or equal angle) are equal.

The vertex angles are equal.

The outer angle of a triangle is equal to the sum of two non-adjacent inner angles.

Two straight lines perpendicular to the same straight line in the same plane are parallel lines.

The same angle is equal and two straight lines are parallel.

The bisector of the top angle, the height on the bottom edge and the midline on the bottom edge of the isosceles triangle coincide with each other. In a right triangle, the center line of the hypotenuse is equal to half of the hypotenuse.

A point on the bisector of an angle is equal to the distance on both sides of the angle. And its inverse theorem.

The parallel segments sandwiched between two parallel lines are equal. The vertical segments sandwiched between two parallel lines are equal.

A set of parallelograms with parallel and equal opposite sides, or two sets of opposite sides are equal respectively, or the diagonal is bisected.

A quadrilateral with three right angles and a parallelogram with equal diagonals are rectangles.

Diamond nature: four sides are equal, diagonal lines are perpendicular to each other, and each diagonal line bisects a set of diagonal lines.

The four corners of a square are right angles and the four sides are equal. The two diagonals are equal and bisected vertically, and each diagonal bisects a set of diagonals.

If a pair of two central angles, two arcs, two chords, and the center distance between two chords are equal in the same circle or in the same circle, other corresponding quantities are equal.

The diameter perpendicular to the chord bisects the chord and bisects the arc opposite to the chord. The diameter (not the diameter) that bisects the chord is perpendicular to the chord and bisects the arc opposite the chord.

The two right triangles divided by the high line on the hypotenuse are similar to the original triangle.

The ratio of similar triangles to the high line, the ratio to the center line and the ratio to the angular bisector are all equal to the similarity ratio. The ratio of similar triangles area is equal to the square of similarity ratio.

The diagonal lines of the circle inscribed with the quadrilateral are complementary, and any external angle is equal to its internal angle.

The judgment theorem of tangent passes through the outer end of the radius, and the straight line perpendicular to this radius is the tangent of the circle.

The property theorem of tangent ① A straight line whose center is perpendicular to the tangent must pass through the tangent point. ② The tangent of the circle is perpendicular to the radius passing through the tangent point. ③ The straight line perpendicular to the tangent point must pass through the center of the circle.

The tangent length theorem leads to two tangents of a circle from a point outside the circle, and their tangent lengths are equal. The straight line connecting a point outside the circle and the center of the circle bisects the angle between two tangents from that point to the circle.

The degree of the chord tangent angle is equal to half the degree of the arc it encloses. The tangent angle is equal to the circumferential angle of the arc it encloses.

Intersecting chord theorem; Cutting line theorem; secant theorem

A circle is a central symmetrical figure with the center of the circle as the symmetrical center; Any rotation angle α around the center of the circle can coincide with the original.

The angle of the vertex at the center of the circle is called the central angle. The distance from the center of the circle to the chord is called the chord center distance.

Circular Power Theorem (Intersection Theorem, Secant Theorem and Their Inference (Secant Theorem) are collectively called Circular Power Theorem)

Tangent length theorem

Vertical diameter theorem, circle angle theorem and chord tangent angle theorem.

Four-circle theorem

In the same circle or in the same circle, equal central angles have equal arcs, equal chords and equal chord-center distances.

In the same circle or in the same circle, if one of two central angles, two arcs, two chords or the distance between two chords is equal, the corresponding other components are equal.

Divide the whole circumference into 360 equal parts, and each arc is 1. The degree of the central angle is equal to the degree of the arc it faces.

A circle is a figure with central symmetry, that is, it can coincide with the original figure after rotating180 around its symmetrical center (center). This attribute is not difficult to understand. Different from other figures with symmetrical centers, the circle also has rotation invariance, that is, it can coincide with the original figure by rotating at any angle around its center.

The vertical diameter theorem bisects the chord perpendicular to its diameter and bisects the two arcs opposite the chord.

(1) bisects the diameter of the chord (not the diameter) perpendicular to the chord and bisects the two arcs opposite the chord.

(2) The perpendicular line of the chord passes through the center of the circle and bisects the two arcs opposite to the chord.

(3) bisect the diameter of an arc opposite to the chord, bisect the chord vertically, and bisect another arc opposite to the chord.

Two parallel chords of a circle have equal arcs.

(1) An arc subtends a circumferential angle equal to half the central angle it subtends.

(2) The circumferential angles of the same arc or equal arc are equal; In the same circle or in the same circle, the arcs with equal circumferential angles are also equal.

(3) The circumference angle (or diameter) of a semicircle is a right angle; A chord with a circumferential angle of 90 is a diameter.

(4) If the median line of one side of a triangle is equal to half of this side, then this triangle is a right triangle.

(1) A circle is an axisymmetric figure, and every straight line passing through the center of the circle is its axis of symmetry.

(2) The diameter perpendicular to the chord bisects the chord and bisects the two arcs opposite to the chord.

(3) The diameter of bisecting the chord (not the diameter) is perpendicular to the chord and bisects the two arcs opposite the chord.

(4) The perpendicular bisector of a chord bisects two opposite chords through the center of the circle.

(5) bisect the diameter of an arc opposite to the chord, bisect the chord vertically, and bisect another arc opposite to the chord.

(6) The number of radians between two parallel chords of a circle is equal.

A circle is an axisymmetric figure, and every straight line passing through the center of the circle is its axis of symmetry.

The diameter perpendicular to the chord bisects the chord and bisects the two arcs opposite the chord.

The diameter (not the diameter) that bisects the chord is perpendicular to the chord and bisects the two arcs opposite the chord.

In the same circle or in the same circle, the arcs with equal central angles are equal, the chords are equal, and the chord center distances of the chords are equal.

In the same circle or in the same circle, equal chords have equal arcs, equal central angles and equal distances between chords.

The same arc has countless relative circumferential angles.

The ratio of arcs is equal to the ratio of the central angles of arcs.

Diagonal complementation or equality of inscribed quadrangles of a circle.

Three points that are not on a straight line can determine a circle.

The diameter is the longest chord in a circle.

Chords divide the circle into upper and lower arcs.

chemistry

This was once sent to me by a netizen-I wonder if it will be useful to you.

First, the colors of common substances in junior high school chemistry

(1) color of solid

1, red solid: copper, iron oxide 2, green solid: basic copper carbonate 3, blue solid: copper hydroxide, copper sulfate crystal 4, purple-black solid: potassium permanganate 5, light yellow solid: sulfur.

6. Colorless solids: ice, dry ice and diamonds.

7. Silvery white solids: metals such as silver, iron, magnesium, aluminum and mercury.

8. Black solids: iron powder, charcoal, copper oxide, manganese dioxide and ferroferric oxide (carbon black, activated carbon).

9. Red-brown solid: iron hydroxide 10, white solid: sodium chloride, sodium carbonate, sodium hydroxide, calcium hydroxide, calcium carbonate, calcium oxide, copper sulfate, phosphorus pentoxide, magnesium oxide (II) and liquid color.

1 1, colorless liquid: water, hydrogen peroxide 12, blue solution: copper sulfate solution, copper chloride solution and copper nitrate solution.

13, light green solution: ferrous sulfate solution, ferrous chloride solution, ferrous nitrate solution.

14. Yellow solution: ferric sulfate solution, ferric chloride solution and ferric nitrate solution.

15, purplish red solution: potassium permanganate solution

16, purple solution: litmus solution

(3) Color of gas

17, red-brown gas: nitrogen dioxide 18, yellow-green gas: chlorine.

Colorless gases: oxygen, nitrogen, hydrogen, carbon dioxide, carbon monoxide, sulfur dioxide, hydrogen chloride gas and most other gases.

Second, the acidity and alkalinity of junior high school chemical solution is 1. Acidic solution: acidic solution and some salt solutions (sodium bisulfate, potassium bisulfate, etc. ).

2. Alkaline solution: alkaline solution and some salt solutions (sodium carbonate, sodium bicarbonate, etc. )

3. Neutral solution: water and most salt solutions.

Junior high school chemistry is exposed to air quality changes.

The quality has improved.

1, increased by water absorption: sodium hydroxide solid, calcium chloride, magnesium chloride and concentrated sulfuric acid;

2. Increase due to reaction with water: calcium oxide, barium oxide, potassium oxide, sodium oxide and copper sulfate;

3. Increase due to reaction with carbon dioxide: sodium hydroxide, potassium hydroxide, barium hydroxide and calcium hydroxide;

(2) the quality is reduced.

1, reduced by volatilization: concentrated hydrochloric acid, concentrated nitric acid, alcohol, gasoline and concentrated ammonia water;

2. Decrease due to weathering: sodium carbonate crystals.

Four, junior high school chemical inspection

(a), gas inspection

1, oxygen: put the stick with Mars in the bottle. If the stick is rekindled, it is oxygen.

2. Hydrogen: ignite the gas in the glass tip, cover the small dry and cold beaker, observe whether there are water drops on the glass wall, and pour the clarified limewater into the beaker. If it is not turbid, it is hydrogen.

3. Carbon dioxide: introducing clarified limewater; If it becomes turbid, it is carbon dioxide.

4. Ammonia: wet purple litmus test paper. If the test paper turns blue, it is ammonia.

5, water vapor: through anhydrous copper sulfate, if the white solid turns blue, it contains water vapor.

(2) Inspection of ions.

6. Hydrogen ion: drop purple litmus test solution/add zinc particles 7. Hydroxyl ion: phenolphthalein test solution/copper sulfate solution.

8. Carbonate ion: dilute hydrochloric acid and clear limewater.

9. Chloride ion: silver nitrate solution and dilute nitric acid. If white precipitate is produced, it is chloride ion.

10, sulfate ion: barium nitrate solution and dilute nitric acid/first add dilute hydrochloric acid, then add barium chloride 1 1, ammonium ion: sodium hydroxide solution and heat, and put the wet red litmus test paper on the test tube mouth.

12, copper ion: sodium hydroxide solution is added dropwise, and if blue precipitate is generated, copper ion is generated.

13. Iron ion: drop sodium hydroxide solution, and if reddish-brown precipitate is generated, it is iron ion.

(3) Relevant examples

14. How to check whether NaOH has deteriorated: drop dilute hydrochloric acid, and bubbles will deteriorate.

15. Check whether the quicklime contains limestone: drop dilute hydrochloric acid, and if bubbles are generated, it contains limestone.

16. To test whether NaOH contains NaCl: firstly, drop enough dilute nitric acid, and then drop AgNO3 solution. If a white precipitate appears, it means that it contains NaCl.

17, test three bottles of test solution, namely dilute HNO3, dilute HCl and dilute H2SO4?

Dropping Ba(NO3)2 solution into three test tubes respectively, and if white precipitate is produced, it is dilute H2SO4；; Then drop silver nitrate solution. If white precipitate is produced, it is dilute HCl and the rest is dilute HNO3.

18, starch: add iodine solution, if it turns blue, it means it contains starch.

19, glucose: when adding new copper hydroxide, if brick red cuprous oxide precipitate is generated, it contains glucose.

Five, junior high school chemistry (3)

1. Three major chemical processes in ancient China: papermaking, gunpowder making and porcelain burning.

2. Three oxidation reactions: explosion, combustion and slow oxidation.

3. There are three kinds of particles that make up matter: molecules, atoms and ions.

4. Three kinds of uncharged particles: molecules, atoms and neutrons.

5, material composition and composition of the three statements:

(1), carbon dioxide is composed of carbon and oxygen;

(2) Carbon dioxide is composed of carbon dioxide molecules;

(3) The molecule of carbon dioxide consists of a carbon atom and an oxygen atom.

6. There are three kinds of particles that make up an atom: protons, neutrons and electrons.

7. There are three reasons for water pollution: (1) industrial "three wastes" discharged at will, (2) domestic sewage discharged at will, and (3) pesticides and fertilizers discharged at will.

8. Three methods of collection method: drainage method (water-resistant gas), upward exhaust method (gas with higher density than air) and downward exhaust method (gas with lower density than air).

9. Three invariants of the law of conservation of mass: constant atomic type, constant atomic number and constant atomic mass.

10, three methods of changing unsaturated solution into saturated solution:

Increase solute, decrease solvent and change temperature (increase or decrease).

1 1. Three conditions of metathesis reaction: water, gas or precipitation.

12, nitrogen, phosphorus and potassium fertilizers.

13. Three gaseous pollutants discharged into the air: carbon monoxide, nitrogen oxides and sulfur oxides.

14, burning white light-emitting substances: magnesium bars, charcoal, candles (carbon dioxide and water).

15. Flammable and reducible substances: hydrogen, carbon monoxide and elemental carbon.

16. These three combustible gases are: hydrogen (ideal), carbon monoxide (toxic) and methane (common).

17 and three chemical properties of CO: flammability, reducibility and toxicity.

18, three major fossil fuels: coal, oil and natural gas. (All mixtures)

19, three ferrous metals: iron, manganese and chromium.

20. Three oxides of iron: ferrous oxide, iron oxide and ferric oxide.

2 1. Three oxides in ironmaking: iron ore, coke and limestone.

22. Three common strong acids: hydrochloric acid, sulfuric acid and nitric acid.

23. Three characteristics of concentrated sulfuric acid: water absorption, dehydration and strong oxidation.

24. Three common names of sodium hydroxide: caustic soda, caustic soda and caustic soda.

25. The basic copper carbonate is decomposed by heat to produce three oxides: copper oxide, water (hydrogen peroxide) and carbon dioxide.

26. Three substances that cannot be used to prepare CO2 in the laboratory: nitric acid, concentrated sulfuric acid and sodium carbonate.

27. Three flames of alcohol lamp: inner flame, outer flame and flame core.

28. There are three prohibitions on the use of alcohol lamps: it is forbidden to add alcohol to a burning lamp, it is forbidden to light another alcohol lamp with one alcohol lamp, and it is forbidden to blow out the alcohol lamp with your mouth.

29. The three functions of glass rods in the purification of raw salt: stirring, drainage and transfer.

30. Three inclinations in liquid filtration operation: (1) When pouring filtrate, the beaker mouth is close to the glass rod, (2) the glass rod is slightly close to one end of the three-layer filter paper, and (3) the nozzle at the lower end of the funnel is close to the inner wall of the beaker.

Three steps of 3 1. solid solution preparation: calculation, weighing and dissolution.

32. Three steps of concentration and dilution: calculation, measurement and dissolution.

33. Three instruments: beaker, measuring cylinder and glass rod.

34. Three substances that give off heat when meeting water: concentrated sulfuric acid, sodium hydroxide and quicklime.

35. The reason why the filtrate is still turbid after filtering twice: the filter paper is damaged, the instrument is not clean, and the liquid level is higher than the edge of the filter paper.

36. Three principles of medication: Don't touch drugs with your hands, don't put your nostrils to the mouth of the container to smell the drugs, and don't taste any drugs.

37. Three meanings of metal active sequence: (1) The higher the position of metal, the easier it is to lose electrons and become ions in aqueous solution, and the stronger its activity; (2) The metal before hydrogen can replace the hydrogen in acid, and the metal behind hydrogen cannot replace the hydrogen in acid; (3) The former metals can replace the latter metals from their salt solutions.

38. Effect of temperature on solid solubility: (1) The solubility of most solid substances increases with the increase of temperature; (2) The solubility of a few solid substances is not affected by temperature; (3) The solubility of a few solid substances decreases with the increase of temperature.

39. Factors affecting the dissolution rate: (1) temperature, (2) whether stirring, and (3) the size of solid particles.

40. Three substances make iron rust: iron, water and oxygen.

4 1, three states of solute: solid, liquid and gas.

42. There are three factors that affect solubility: the nature of solute, the nature of solvent and temperature.

Six, an important part of the common mixture of junior high school chemistry.

1. Air: nitrogen (N2) and oxygen (O2).

2. Water gas: carbon monoxide (CO) and hydrogen (H2)

3. Gas: carbon monoxide (CO)

4. Natural gas: methane (CH4)

5. Limestone/marble: (CaCO3)

6. Pig iron/steel: (iron)

7. Charcoal/coke/carbon black/activated carbon: (c)

8. Rust: (Fe2O3)

Seven, junior high school chemistry common substances commonly known as

1 sodium chloride: salt

2. Sodium carbonate (Na2CO3): soda ash, soda ash and caustic soda; 3. Sodium hydroxide (NaOH): caustic soda, caustic soda and caustic soda.

4. Calcium oxide: quicklime

5. Calcium hydroxide (Ca(OH)2): hydrated lime, hydrated lime.

6. Carbon dioxide solid (CO2): dry ice.

7. HCl: hydrochloric acid

8. Basic copper carbonate (Cu2(OH)2CO3): patina 9. Copper sulfate crystal (CuSO4 .5H2O): blue alum, sulfuric acid 10, methane (CH4): biogas.

1 1 ethanol (C2H5OH): alcohol.

12, acetic acid (CH3COOH): acetic acid

13 hydrogen peroxide (H2O2): hydrogen peroxide

14, mercury: mercury

15, sodium bicarbonate (NaHCO3): baking soda eight. Impurity removal of substances

1, CO2(CO): passing gas through hot copper oxide,

2.CO(CO2): Through sufficient sodium hydroxide solution.

3.H2 (water vapor): through concentrated sulfuric acid/through sodium hydroxide solid.

4.CuO(C): Burning the mixture in air (in oxygen flow).

5. Cu(Fe): add enough dilute sulfuric acid 6. Cu(CuO): add enough dilute sulfuric acid.

7.FeSO4(CuSO4): Add enough iron powder.

8.NaCl(Na2CO3): Add enough hydrochloric acid.

9.NaCl(Na2SO4): Add enough barium chloride solution.

10, NaCl(NaOH): add enough hydrochloric acid.

1 1, NaOH(Na2CO3): add enough calcium hydroxide solution.

12, NaCl(CuSO4): add enough barium hydroxide solution.

13, NaNO3(NaCl): add enough silver nitrate solution.

14, NaCl(KNO3): evaporating solvent.

15, KNO3(NaCl): saturated solution of cooling heat.

16, CO2 (steam): through concentrated sulfuric acid.

Nine, the most in chemistry

1, the most ideal fuel in the future is H2.

2. The simplest organic matter is CH4.

3. The lowest density gas is H2.

4. The substance with the smallest relative molecular mass is H2.

5. The oxide with the smallest relative molecular mass is H2O.

6. The smallest particle in a chemical change is an atom.

7. When pH = 0, the acidity is the strongest and the alkalinity is the weakest.

When PH= 14, the alkalinity is the strongest and the acidity is the weakest.

8. Nitrogen, potassium and phosphorus are the most scarce elements in soil, and urea is the most effective nitrogen fertilizer.

9. The hardest substance in nature is diamond.

10, China was the first country to use natural gas.

1 1. The most abundant element in the earth's crust is oxygen.

12, the most abundant metal element in the earth's crust is aluminum.

13. Nitrogen is the most abundant gas in the air.

14. The most abundant element in the air is nitrogen.

15. The three most important fossil fuels in the world today are coal, oil and natural gas.

16, the element that forms the most compounds: carbon.

X. related differences

1, the physical properties of diamond and graphite are different because of the different arrangement of carbon atoms.

2. The properties of pig iron and steel are different: this is because the carbon content is different.

The chemical properties of carbon monoxide and carbon dioxide are different: that's because the molecular composition is different.

The chemical properties of oxygen and ozone are different because of their different molecular compositions. The chemical properties of water and hydrogen peroxide are different because of their different molecular compositions. )

4. Different types of elements: because the number of protons is different.

5. The valence of elements is different: it is because the number of electrons in the outermost layer is different.

6. The chemical properties of sodium atom and sodium ion are different: it is because the number of electrons in the outermost layer is different.

XI: Toxic substances

1, toxic solids: sodium nitrite (NaNO2), lead acetate, etc.

2. Toxic liquids: mercury, copper sulfate solution, methanol, solution containing Ba2+ (except baso4);

3. Toxic gases: carbon monoxide, nitrogen oxides and sulfur oxides.

XII: Laboratory Methods

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1, laboratory oxygen: 2kmno4 = = = = 2k2mno4+MnO2+O2 =

manganese dioxide

2 kclo 3 = = = = = = = 2 KCl+3 O2↓