3。 The vertex angles are equal.

5。 The outer angle of a triangle is equal to the sum of two non-adjacent inner angles.

6。 Two straight lines perpendicular to the same straight line in the same plane are parallel lines.

7。 The same angle is equal and two straight lines are parallel.

12。 The bisector of the top angle, the height on the bottom edge and the midline on the bottom edge of the isosceles triangle coincide with each other.

16。 In a right triangle, the center line of the hypotenuse is equal to half of the hypotenuse.

19。 A point on the bisector of an angle is equal to the distance on both sides of the angle. And its inverse theorem.

2 1。 The parallel segments sandwiched between two parallel lines are equal. The vertical segments sandwiched between two parallel lines are equal.

22。 A set of parallelograms with parallel and equal opposite sides, or two sets of opposite sides are equal respectively, or the diagonal is bisected.

24。 A quadrilateral with three right angles and a parallelogram with the same diagonal are rectangles.

25。 Diamond nature: four sides are equal, diagonal lines are perpendicular to each other, and each diagonal line bisects a set of diagonal lines.

27。 The four corners of a square are right angles and the four sides are equal. The two diagonals are equal and bisected vertically, and each diagonal bisects a set of diagonals.

34。 If a pair of two central angles, two arcs, two chords, and the center distance between two chords are equal in the same circle or in the same circle, other corresponding quantities are equal.

36。 The diameter perpendicular to the chord bisects the chord and bisects the arc opposite to the chord. The diameter (not the diameter) that bisects the chord is perpendicular to the chord and bisects the arc opposite the chord.

43。 The two right triangles divided by the high line on the hypotenuse are similar to the original triangle.

46。 The ratio of similar triangles to the high line, the ratio to the center line and the ratio to the angular bisector are all equal to the similarity ratio. The ratio of similar triangles area is equal to the square of similarity ratio.

37. The diagonals of the quadrilateral inscribed in the circle are complementary, and any external angle is equal to its internal angle.

47。 The judgment theorem of tangent passes through the outer end of the radius, and the straight line perpendicular to this radius is the tangent of the circle.

48。 The property theorem of tangent ① A straight line whose center is perpendicular to the tangent must pass through the tangent point. ② The tangent of the circle is perpendicular to the radius passing through the tangent point. ③ The straight line perpendicular to the tangent point must pass through the center of the circle.

49。 The tangent length theorem leads to two tangents of a circle from a point outside the circle, and their tangent lengths are equal. The straight line connecting a point outside the circle and the center of the circle bisects the angle between two tangents from that point to the circle.

50。 The degree of the chord tangent angle is equal to half the degree of the arc it encloses. The tangent angle is equal to the circumferential angle of the arc it encloses.