Prove:

Take GB midpoint m, CG midpoint n, BM=MG ①.

Connecting MN, ND, DE, EM

Because DE is the center line of △ABC.

So Germany//BC, Germany =/bc2 (2)

And MN is the center line of △BCG.

So MN//BC, MN=BC/2 ③.

DE//BC is obtained from ② ③, and DE = BC.

A quadrilateral is a parallelogram.

So MG=GD[ parallelogram diagonal bisects each other] ④

MB=MG=GD comes from ① ④.

So GB=MB+MG=GD+GD=2GD.

(2)AF passes through G point. Because point G is the center of gravity of the triangle and the intersection of three sides of the triangle.

Combing the knowledge of mathematical parallelogram in the second day of junior high school

Emphasis: the nature and judgment of parallelogram.

Difficulties: Comprehensive application and judgment of parallelogram properties.

Knowledge point 1: the definition of parallelogram

Definition of parallelogram: Two groups of parallelograms with parallel opposite sides are called parallelograms. That is, in a quadrilateral ABCD, if there are AB∨CD and AD∨BC, the quadrilateral ABCD is a parallelogram.

Key points: the representation of parallelogram: the symbol □ is used for parallelogram.

Related concepts: in parallelogram, adjacent edges and adjacent angles are called adjacent edges and adjacent angles respectively; Non-adjacent edges and corners are called opposite edges and diagonal corners respectively.

Knowledge point 2: the nature of parallelogram

1. Viewed from the side, the two groups of parallelograms are parallel and equal;

2. From the point of view, the adjacent angles of parallelogram are complementary and the diagonal angles are equal;

3. Looking sideways, the diagonal of the parallelogram is equally divided;

4. The parallelogram is a central symmetric figure, and the intersection of diagonal lines is the center of symmetry;

5. If a straight line passes through the intersection of two diagonals of a parallelogram, the line segment cut by a group of opposite sides of the straight line takes the intersection of the diagonals as the center, and the straight line bisects the area of the parallelogram.

6. The diagonal of the parallelogram is divided into four triangles with equal products.

Knowledge point 3: the judgment of parallelogram

1, viewed from the side

(1) Two groups of parallelograms with parallel opposite sides are parallelograms.

(2) Two groups of quadrangles with equal opposite sides are parallelograms.

(3) A set of quadrilaterals with parallel and equal opposite sides is a parallelogram.

2. Viewed from the angle, two groups of quadrangles with equal diagonal are parallelograms.

3. Seen from the diagonal, the quadrilateral whose diagonal lines bisect each other is a parallelogram.