Mathematical Theorem Relation Theorem of Three Sides of a Triangle: The sum of two sides of a triangle is greater than the third side. Inference: The difference between two sides of a triangle is smaller than the third side, and the sum of three angles of the triangle is equal to 180. Inference 1. The two acute angles of a right triangle are complementary. Inference 2. One outer angle of a triangle is equal to two non-adjacent inner angles, inference 3. The heavy rain in one outer corner of the triangle is not adjacent to it. The property theorem of angular bisector is that the distance from a point on the angular bisector to both sides of the angle is equal. Geometric language: ∫oc is ∠AOB (or ∠ AOC = ∠ BOC) PE ⊥ OA, PF⊥OB point P is on OC ∴ PE = PF (. PF ⊥ OBPE = PF ∴ Point P is on the bisector of ∠AOB (judgment theorem of angle bisector). Property theorem of isosceles triangle. The two base angles of an isosceles triangle are equal. Geometric language: ∵ AB = AC ∴∠ B = ∠ C (equilateral and equilateral). BD = DC ∴∠ 1 = ∠ 2, AD⊥BC (the bisector of the top angle of an isosceles triangle bisects the bottom vertically) (2) ∵ AB = AC, ∠1= ∠ 2 ∴. Then the opposite sides of these two angles are also equal. Geometric language: ∵∠ B = ∠ C ∴ AB = AC (equilateral) inference 1 A triangle with three equal angles is equilateral. Geometric language: ∵∠A =∠B =∞. ∠ A = 60 (∠ B = 60 or ∠ C = 60) ∴ AB = AC = BC (an isosceles triangle with an angle equal to 60 is an equilateral triangle) Inference 3 In a right triangle, if an acute angle is equal to 30, the right side it faces is equal to half of the hypotenuse. Then the right-angled side it faces is equal to half of the hypotenuse. ) The distance between the point on the vertical line and the two endpoints of a line segment is equal in the theorem of the median vertical line of a line segment. Geometric language: ∵MN⊥AB in C, AB = BC, (MN bisects AB vertically) point P is any point in MN.