Length unit conversion
1 km = 1 000m1m = 10 decimeter.
1 decimeter =10cm1m =10cm.
1 cm = 10/0mm
Area unit conversion
1 km2 = 100 hectare
1 ha = 1 10,000 m2
1 m2 = 100 square decimeter
1 square decimeter = 100 square centimeter
1 cm2 = 100 mm2
Conversion formula of volume (volume) product unit
1 m3 = 1000 cubic decimeter
1 cubic decimeter = 1000 cubic centimeter
1 cubic decimeter = 1 liter
1 cm3 = 1 ml
1 m3 = 1000 liter
Weight unit conversion
1 ton = 1000 kg
1 kg =1000g
1 kg = 1 kg
2.2022 Summary of Mathematical Formulas in Volume II of Grade 3
1.① The outer distance between two circles is d-r+r+r; (2) circumscribed circle d d = r+r; ③ two circles intersect r-r \ u d \ u r+r (r \ u r); (4) Two circles are inscribed with d = r-r (r-r) (5) Two circles contain d-r-r (r-r).
2. Theorem The radius and vertex of a regular N-polygon divide the regular N-polygon into 2n congruent right triangles.
3. The area Sn=pnrn/2p of the regular N-polygon represents the perimeter of the regular N-polygon.
4. If there are k positive N corners around a vertex, since the sum of these corners should be 360, then K× (n-2) 180/n = 360 becomes (n-2)(k-2)=4.
5. Sector area formula: s sector =n∏R/360=LR/2.
6. Inner common tangent length =d-(R-r) Outer common tangent length =d-(R+r).
7. It follows that if the arc sandwiched by two chord angles is equal, then the two chord angles are also equal.
8. The interior of a circle can be regarded as a collection of points whose center distance is less than the radius.
9. similar triangles's theorem 1 Two angles are equal and two triangles are similar (ASA).
10. The trapezoid midline theorem is parallel to the two bottoms and equal to half of the sum of the two bottoms. L = (a+b) ÷ 2s = l× h.
1 1. rhombic area = half of diagonal product, that is, S=(a×b)÷2.
12. The sum of the internal angles of the polygon and Theorem n is equal to (n-2) × 180.
13. Inverse Theorem of Pythagorean Theorem If the lengths of three sides of a triangle A, B and C are related and a+b=c, then this triangle is a right triangle.
14. Pythagorean theorem The sum of squares of two right angles A and B of a right triangle is equal to the square of the hypotenuse C, that is, A+B = C.
15. The property theorem of isosceles triangle. The two base angles of an isosceles triangle are equal.
3.2022 Summary of Mathematical Formulas in Volume II of Grade 3
(1) geometric series: a(n+ 1)/an=q(n∈N).
(2) General formula: an = a1× q (n-1);
Generalization: an = am× q (n-m);
① if m, n, p, q∈N, m+n=p+q, then am _ an = ap _ aq.
(2) In geometric series, every k term is added in turn and still becomes a geometric series.
③ If m, n, q∈N and m+n=2q, then am _ an = AQ 2.
(5) "G is the equal ratio mean of A and B" and "G 2 = AB (G ≠ 0)".
(6) In geometric series, the first term a 1 and the common ratio q are not zero.
Note: In the above formula, an stands for the nth term of geometric series.
4.2022 Summary of Mathematical Formulas in Volume II of Grade 3
1. Three points that are not on the same straight line determine a circle.
2. The vertical diameter theorem bisects the chord perpendicular to its diameter and bisects the two arcs opposite the chord.
Inference 1
(1) bisects the diameter (not the diameter) of the chord perpendicular to the chord and bisects the two arcs opposite to 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.
Inference 2 The arcs between two parallel chords of a circle are equal.
3. A circle is a central symmetrical figure with the center of the circle as the symmetrical center.
4. A circle is a set of points whose distance from a fixed point is equal to a fixed length.
5. The interior of a circle can be regarded as a collection of points whose center distance is less than the radius.
6. The outside of a circle can be regarded as a collection of points whose center is farther than the radius.
7. The same circle or the same circle has the same radius.
8. The distance to a fixed point is equal to the trajectory of a fixed-length point, which is a circle with the fixed point as the center and the fixed length as the radius.
9. Theorem In the same circle or in the same circle, the isocentric angle has equal arc, chord and chord center distance.
10. It is inferred that in the same circle or equal circle, if one set of quantities in two central angles, two arcs, two chords or the chord-center distance between two chords is equal, the corresponding other set of quantities is also equal.
1 1 Theorem The diagonals of the inscribed quadrilateral of a circle are complementary, and any external angle is equal to its internal diagonal.
12.① intersection point d of straight line l and ⊙O
(2) the tangent of the straight line l, and ⊙ o d = r.
③ Lines L and ⊙O are separated from each other d>r.
13. The judgment theorem of tangent is that the outer end of the radius and the straight line perpendicular to this radius are the tangents of the circle.
14. The property theorem of tangent. The tangent of a circle is perpendicular to the radius passing through the tangent point.
15. Inference 1 A straight line passing through the center of the circle and perpendicular to the tangent must pass through the tangent point.
16. Inference 2 A straight line that crosses the tangent point and is perpendicular to the tangent must pass through the center of the circle.
17. The tangent length theorem leads to two tangents of a circle from a point outside the circle. Their tangents are equal in length, and the connecting line between the center of the circle and this point bisects the included angle between the two tangents.
18. The sum of two opposite sides of the circumscribed quadrangle of a circle is equal, and the outer angle is equal to the inner diagonal.
19. If two circles are tangent, then the tangent point must be on the line.
20.① Two circles are separated by d>. R+r
(2) circumscribed circle d d = r+r.
(3) the intersection of two circles R-rr)
④ inscribed circle d = r-r (r >); R) (5) Two circles contain dr)
5.2022 Summary of Mathematical Formulas in Volume II of Grade Three
1. There is only one straight line between two points.
2. The shortest line segment between two points.
3. The complementary angles of the same angle or equal angle are equal.
4. The complementary angles of the same angle or equal angle are equal.
5. There is one and only one straight line perpendicular to the known straight line.
6. Of all the line segments connecting a point outside the straight line with points on the straight line, the vertical line segment is the shortest.
7. The axiom of parallelism passes through a point outside a straight line, and one and only one straight line is parallel to this straight line.
8. If two straight lines are parallel to the third straight line, the two straight lines are also parallel to each other.
9. The same angle is equal and two straight lines are parallel.
10. The internal dislocation angles are equal and the two straight lines are parallel.
1 1. The inner angles on the same side are complementary and the two straight lines are parallel.
12. Two straight lines are parallel and have the same angle.
13. Two straight lines are parallel and the internal dislocation angles are equal.
14. Two straight lines are parallel and complementary.
15. Theorem The sum of two sides of a triangle is greater than the third side.
16. Inference that the difference between two sides of a triangle is smaller than the third side.
17. The sum of the internal angles of the triangle is equal to 180.
18. It is inferred that the two acute angles of 1 right triangle are complementary.
19. Inference 2 An outer angle of a triangle is equal to the sum of two non-adjacent inner angles.
20. Inference 3 The outer angle of a triangle is larger than any inner angle that is not adjacent to it.