Chapter 11 Review of congruent triangles

Congruent triangle

1. Definition: Two triangles that can completely coincide are called congruent triangles.

Understanding: ① The shape and size of congruent triangles are completely equal, regardless of location; ② A triangle can be translated, folded and rotated to get its congruence; ③ The congruence of triangle does not change with the change of position.

2. What is the nature of congruent triangles?

(1) congruent triangles has equal sides and angles.

Understanding: ① Long side to long side, short side to short side; Maximum angle to maximum angle and minimum angle to minimum angle; ② The opposite side of the corresponding angle is the corresponding edge, and the angle of the corresponding edge pair is the corresponding angle.

(2) The circumference and area of congruent triangles are equal.

(3) The corresponding median line, angular bisector and high line on the corresponding side of congruent triangles are equal respectively.

3. congruent triangles's judgment

Edge: Three edges correspond to the coincidence of two triangles (abbreviated as "SSS")

Angle: Two sides and their included angles are equal. Two triangles are congruent (abbreviated as "SAS").

Corner: Two triangles coincide with two corners and their clamping edges (abbreviated as "ASA").

Corner edge: the opposite side of two angles and one angle corresponds to the congruence of two triangles (abbreviated as "AAS")

Bevel. Right-angled side: the hypotenuse and a right-angled side correspond to the congruence of two right-angled triangles (abbreviated as "HL").

4. The basic idea of proving the coincidence of two triangles:

Second, the bisector of an angle: draw a ray from the vertex of an angle to divide the angle into two equal angles. This ray is called the bisector of this angle.

1, property: the distance between the point on the bisector of the angle and both sides of the angle is equal.

2. Judgment: The point with equal distance from the inside of the corner to both sides of the corner is on the bisector of the corner.

Three, learning congruent triangles should pay attention to the following questions:

(1) The different meanings of "corresponding edge" and "opposite edge", "corresponding angle" and "diagonal" should be correctly distinguished;

(2) When two triangles are congruent, the letters representing the corresponding vertices should be written in the corresponding positions;

(3) Two triangles with "three corresponding angles are equal" or "two opposite corners have two sides and one of them is equal" are not necessarily the same;

(4) Always pay attention to the implicit conditions in graphics, such as "corner", "edge" and "diagonal".

(5) Prove triangle congruence by truncated complementary method.

Chapter 12 Axisymmetric

A, axisymmetric graphics

1. Fold the chart along a straight line. If the parts on both sides of a straight line can completely overlap, then this graph is called an axisymmetric graph. This straight line is its axis of symmetry. At this time, we also say that this figure is symmetrical about this straight line (axis).

2. Fold the chart along a straight line. If it can completely coincide with another figure, the two figures are said to be symmetrical about this line. This straight line is called the axis of symmetry. The point that overlaps after folding is the corresponding point, which is called the symmetrical point.

3. The difference and connection between axisymmetric figure and axisymmetric figure.