Sorting out the knowledge points of Olympiad geometry in primary schools [three chapters]

# Elementary Olympiad # Introduction The sky is high and the sea is wide, and the fish jumps. Learn this stage, show your unique brilliance, make good use of every minute, accumulate a little knowledge, solve difficult problems and learn to draw inferences from others. The following is "Three Questions and Answers of Elementary School Mathematics Olympic Geometry Knowledge Points" for your reference.

Part one: Cognition of geometric figures.

Part II: Common Theorems

The bird's head theorem is the angle theorem.

Dovetail theorem is a kind of * * * edge theorem.

* * * Angle theorem:

If two triangles have a set of equal or complementary corresponding angles, their area ratio is equal to the ratio of the products of the two sides of the corresponding angles.

* * * Edge Theorem:

A triangle with a common side is called a * * * side triangle.

* * * Edge Theorem: Let straight lines AB and PQ intersect M, then S△PAB/S△QAB=PM/QM.

Most of these theorems use the method of similar graphics, but similar graphics have not been learned in primary school, so it is a little difficult for children to introduce these in primary school Olympics.

In order to avoid similarity, we use the corresponding base-height ratio to derive the triangle area ratio.

For example, the dovetail theorem, in a triangle ABC, D is the bisector of BC, close to point B, connecting AD, E is a point on AD, and connecting EB and EC, four triangles can be obtained.

Obviously, the area ratio of triangle ABD to ACD is 1: 2.

Because * * * here, the ratio of the two corresponding heights is 1: 2.

And four small triangles will have a similar relationship.

The area ratio of triangle ABE to triangle ACE is 1: 2.

The area ratio of triangular bed and triangular CED is also 1: 2.

So the area ratio of triangle ABE and triangle ACE is equal to the area ratio of triangle BED and triangle CED, which is the legendary dovetail theorem.

The above is based on the proof that the ratio of height is equal to the ratio of triangle area behind * * * *.

Be sure to recite it. As long as you know how to transform, you can do it. As for the bird head theorem, don't memorize it by rote. If you master the principle, it will be handy to use.

Part III: Plane Graphics

1, rectangle

(1) function

A quadrilateral with equal opposite sides and four right angles. There are two axes of symmetry.

(2) Calculation formula

c=2(a+b)

s=ab

2. Square

(1) Function:

A quadrilateral with four equal sides and four right angles. There are four axes of symmetry.

(2) Calculation formula

c=4a