1. Trilateral relation of triangle: the sum of any two sides is greater than the third side, and the difference between any two sides is less than the third side.
2. Let three sides of a triangle be A, B and C, then A+B >; c，a & gtc-b，b+ c & gt； a，b & gta-c，a+c & gt； b，c & gtb-a
3. Example: any △ABC, verifying AB+AC > In 200 BC.
Proof: Take AD=AC on the extension line of BA.
Then ∠D=∠ACD (equilateral and equiangular)
∵∠BCD & gt； ∠ACD
∴∠bcd>； ∠D
∴bd>； BC (large angle to large side)
∫BD = a b+ AD = a b+ AC
∴ab+ac>； B.C.
Extended data:
special
right triangle
Property 1: The sum of squares of two right angles of a right triangle is equal to the square of the hypotenuse.
Property 2: In a right triangle, two acute angles are complementary. ?
Property 3: In a right triangle, the median line on the hypotenuse is equal to half of the hypotenuse.
Property 4: The product of two right angles of a right triangle is equal to the product of the hypotenuse and the height of the hypotenuse.
Sine relation:
Historically, the geometric derivation methods of sine theorem are rich and colorful. According to its thinking characteristics, it can be mainly divided into two types.
The first method, which can be called "equal diameter method", was first adopted by Arab mathematician and astronomer Nasir Ear Nail in the 3rd century A.D./Kloc-0 and German mathematician Rejo Montanus in the 5th century A.D./Kloc-0. "Equal Diameter Method" regards the sine of two internal angles of a triangle as a sine line on a circle with the same radius (before16th century, trigonometric function was regarded as a line segment instead of a ratio), and the ratio of the two is equal to the ratio of the opposite sides of the angle by using similar triangles property.
Nasir Din extends to the opposite sides of two internal angles at the same time, and the structural radius is larger than the circles on both sides. Reggiomontanus simplified Nasir al-Din's method, and only extended the shorter of the two sides to construct a circle with the same radius as the longer one. From 17 to 18, China mathematician and astronomer Mei Wending and British mathematician Simpson independently simplified the "equal diameter method".