Prove that the angle is equal to 1 and the opposite vertex angle is equal.
2. The complementary angles of an angle (or the same angle) are equal or equal.
3. Two straight lines are parallel, with the same angle and the same internal dislocation angle.
4. All right angles are equal.
5. The two angles divided by the bisector are equal.
6. In the same triangle, equilateral and equiangular.
7. In an isosceles triangle, the height (or midline) of the base bisects the vertex.
8. The diagonals of parallelograms are equal.
9. Each diagonal of the diamond bisects a set of diagonal lines.
10, the two angles on the same base of the isosceles trapezoid are equal.
1 1, Relation Theorem: If two arcs (or chords, or chord distances) are equal in the same circle or equal circle, then the central angles they face are equal.
12. Any external angle of a quadrilateral inscribed with a circle is equal to its internal angle.
13, the circumferential angles of the same arc or equal arc are equal.
14, and the chord tangent angle is equal to the circumferential angle of the arc pair it clamps.
In 15, the same circle or the same circle, if the arcs sandwiched by the two tangent angles are equal, then the two tangent angles are also equal.
16 and congruent triangles have equal angles.
17 and similar triangles have equal angles.
18, use equivalent substitution.
19, use algebra and trigonometry to calculate the degrees with equal angles.
20. Tangent Length Theorem: Two tangents of a circle are drawn from a point outside the circle, and their tangents are equal in length. The connecting line between this point and the center of the circle bisects the included angle of the two tangents.
The main basis and method to prove that a straight line 1 is parallel or vertical and two straight lines are parallel;
Two straight lines defined by (1) that do not intersect in the same plane are parallel.
(2) Parallelism theorem, two straight lines are parallel to the third straight line, and these two straight lines are also parallel to each other.
(3) Determination of parallel lines: the congruence angle is equal (internal dislocation angle or internal angle of the same side), and the two straight lines are parallel.
(4) The opposite sides of the parallelogram are parallel.
(5) The two bottom sides of the trapezoid are parallel.
(6) The midline of a triangle (or trapezoid) is parallel to the third side (or two bottom sides).
(7) If the corresponding line segments cut by two sides of a triangle (or extension lines of two sides) are proportional, the straight line is parallel to the third side of the triangle.
2, the main basis and method to prove that two straight lines are vertical:
(1) Of the four angles formed by the intersection of two straight lines, when one is a right angle, the two straight lines are perpendicular to each other.
(2) The two right angles of a right triangle are perpendicular to each other.
(3) If the two acute angles of a triangle are complementary, the third inner angle is a right angle.
(4) If the median line of one side of a triangle is equal to half of this side, the triangle is a right triangle.
(5) If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the inner angle subtended by this side is a right angle.
(6) The height of one side of a triangle (or polygon) is perpendicular to this side.
(7) The bisector of the top angle of an isosceles triangle (or the median line on the bottom) is perpendicular to the bottom.
(8) The two sides of a rectangle are perpendicular to each other.
(9) Diagonal lines of diamonds are perpendicular to each other.
(10) The diameter (non-diameter) of the bisector is perpendicular to this chord, or the diameter of the arc subtended by the bisector is perpendicular to this chord.
(1 1) The circumferential angle of a semicircle or diameter is a right angle.
(12) The tangent of the circle is perpendicular to the radius of the tangent point.
(13) The line connecting two intersecting circles is perpendicular to the common chord of the two circles.
Congruent triangles decision
Theorem: The sides and angles corresponding to congruent triangles are equal.
Edge Theorem (SAS): Two triangles have two sides, and their included angles are congruent.
Angle Theorem (ASA): Two triangles have two angles and their sides are congruent.
Inference (AAS): Two triangles with two angles and opposite sides of one angle are congruent.
Edge Theorem (SSS): Two triangles corresponding to three equilateral sides are congruent.
Hypotenuse and right-angled edge theorem (HL): Two right-angled triangles with hypotenuse and a right-angled edge are congruent.
Parallelogram property theorem;
1, the diagonals of parallelograms are equal.
2. The opposite sides of the parallelogram are equal.
3. The diagonal of parallelogram is equally divided.
Inference: The parallel segments sandwiched between two parallel lines are equal.
Parallelogram judgment theorem:
1, two sets of quadrangles with equal diagonals are parallelograms.
2. Two groups of quadrilaterals with equal opposite sides are parallelograms.
3. Quadrilaterals whose diagonals are bisected with each other are parallelograms.
4. A set of quadrilaterals with parallel and equal opposite sides is a parallelogram.