Three. Classroom teaching:
[Basic knowledge]
Knowledge structure 1:
Can you prove it?
1. congruent triangles's judgment
Three sides correspond to the coincidence of two equal triangles. (SSS)
Two sides and their included angle correspond to the union of two equal triangles. (SAS)
Two angles and their sides correspond to the congruence of two triangles. (ASA)
The opposite sides of two angles and one angle correspond to the congruence of two equal triangles. (AAS)
2. The nature of congruent triangles
The corresponding edges of congruent triangles are equal, and the corresponding angles are equal.
3. Determination of isosceles triangle
A triangle with two equal angles is an isosceles triangle. (abbreviation: equilateral)
4. The nature of isosceles triangle
The two base angles of an isosceles triangle are equal. (Abbreviation: Equiangular)
The bisector of the top angle, the median line on the bottom edge and the height on the bottom edge of the isosceles triangle coincide with each other. (abbreviation: three lines in one)
5. Determination of equilateral triangle
A triangle with three equilateral sides is an equilateral triangle.
② An isosceles triangle with an angle of 60 is an equilateral triangle.
③ A triangle with three equal angles (all 60) is an equilateral triangle.
6. The nature of right triangle
(1) In a right-angled triangle, if an acute angle is equal to 30, then the right-angled side it faces is equal to half of the hypotenuse.
Inverse theorem: in a right triangle, if a right-angled side is equal to half of the hypotenuse, then the acute angle of this right-angled side is equal to 30.
(2) The median line on the hypotenuse of a right triangle is equal to half of the hypotenuse.
Inverse theorem: If the median line of one side of a triangle is equal to half of this side, then this triangle is a right triangle.
7. Reduce to absurdity.
Assume that the conclusion of the proposition is not valid, and then deduce the results that contradict the definition, axiom, proof theorem or known conditions, thus proving that the conclusion of the proposition must be valid. This method of proof is called reduction to absurdity.
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