The sum of two sides of a triangle is greater than the third side

The difference between two sides of a triangle is less than the third side

As AD⊥BC, the line segment with vertical foot D is called the height of △ABC

Connect the vertex A of △ABC and the midpoint D of the opposite side BC The resulting line segment AD is called the center line of △ABC

Draw the bisector AD of ∠A and intersect the side BC opposite ∠A at point D. The resulting line segment AD is called the angle bisector of △ABC.

The sum of the interior angles of a triangle theorem: The sum of the three interior angles of a triangle is equal to 180°

Two acute angles of a right triangle are complementary to each other

Determination of right triangle

The exterior angle of a triangle is equal to the sum of its two non-adjacent interior angles

The sum of the exterior angles of a triangle is 360°

A closed figure composed of some line segments connected end to end in a plane is called a polygon.

The line segment connecting two non-adjacent vertices of a polygon is called the diagonal of the polygon.

Sum of interior angles of n-sided polygon = (n-2) × 180°

The sum of the exterior angles of a polygon is 360° n×180°-(n-2)×180°

1. Graphics of the same shape and size can be put together Figures that completely overlap are called congruent shapes

2. Two triangles that can completely overlap are called congruent triangles

3. The vertices that overlap two congruent triangles are called The sides that coincide with corresponding vertices are called corresponding angles. The angles that coincide with corresponding vertices are called corresponding angles.

4. Congruent triangles have equal sides and equal angles

5. Congruent triangles have equal areas and equal perimeters

If △ABC≌△A'B'C' then they Corresponding sides are equal Corresponding angles are equal

1. The distance from a point on the bisector of an angle to both sides of the angle is equal 2. The point equidistant from the interior of the angle to both sides of the angle is on the angle bisector.

⑴If a figure is folded along a straight line The parts on both sides of the straight line can overlap each other. This picture The shape is called an axisymmetric figure

⑵ Passing through the midpoint of the line segment and perpendicular to the line segment The straight line is called the perpendicular bisector of the line segment.

⑶If two figures are symmetric about a certain straight line, then The axis of weighing is the perpendicular to the line segment connecting any pair of corresponding points. Bisector

⑷The axis of symmetry of an axially symmetric figure is any pair of corresponding perpendicular bisector of the line segment connected by the points

1. The point on the perpendicular bisector of the line segment and the line segment The distance between two endpoints is equal

2. The point that is equidistant from the two endpoints of the line segment is on this perpendicular bisector of line segment

Axisymmetric graphics in plane rectangular coordinate system

Property 1 The two base angles of an isosceles triangle are equal (Abbreviated as "equilateral equal angles")

Property 2 The vertex bisectors and bases of an isosceles triangle The center line on the side and the height on the bottom coincide with each other (Abbreviated as "three lines in one")

Decision 1 If a triangle has two equal angles, Then the sides opposite these two angles are also equal (Abbreviated as "equal angles and equal sides")

The three interior angles of an equilateral triangle are all equal, And every angle is equal to 60°

Triangles with three equal angles are equilateral triangles

An isosceles triangle with an angle of 60° is an equilateral triangle.

*****In a right triangle, if an acute angle is equal to 30° Then the side of the right angle it opposes is equal to half the hypotenuse