"The Median Theorem of Triangles" PPT courseware

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"The Median Theorem of Triangles" PPT courseware

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The line segment connecting the midpoints of both sides of a triangle is called the median of the triangle

A triangle has three median lines

The median of a triangle is different from the median of a triangle

Concept comparison

(1) Similarities - they are all related to the midpoint of the side;

(2) Differences:

The two endpoints of the median line of a triangle are the midpoints of the sides;

The midline of a triangle has only one endpoint which is the midpoint of the side and the other endpoint which is the vertex of the triangle.

Friendly reminder:

Understand the two meanings of the definition of the median line of a triangle:

① If D and E are the midpoints of AB and AC respectively, then DE is the midpoint of △ABC;

② If DE is the median line of △ABC, then D and E are the midpoints of AB and AC respectively.

Take a guess:

△What is the relationship between the median line DE of △ABC and BC? (guessed from the relationship between position and quantity)

DE∥BC, DE=1/2BC

That is: the median of the triangle is parallel to the third side and equal to half of the third side.

Can you verify your suspicion?

Triangle Median Theorem

The median of a triangle is parallel and equal to half of the third side.

Geometry language:

∵DE is the median line of △ABC

∴DE∥=1/2BC

Purpose

① Prove the parallel problem

② Prove that one line segment is twice or half the length of another line segment

First try

As shown in the figure, in △ABC, D, E, and F are the midpoints of AB, AC, and BC respectively.

①If ∠ADE=65°, then ∠B=___ degree, why?

②If BC=8cm, then DE=?_____cm, why?

③If AC=4cm, BC=6cm, AB=8cm, then the perimeter of △DEF=______

④If the perimeter of △ABC is 24, the perimeter of △DEF is _____

⑤There are _____ parallelograms in the picture

⑥If the area of ​​△ABC is 24, the area of ​​△DEF is _____

Inquiry activities

1. What is the relationship between the perimeter of the triangle surrounded by the three median lines of the triangle and the perimeter of the original triangle?

2. What is the relationship between the area of ​​the triangle surrounded by the three median lines of the triangle and the area of ​​the original triangle?

expand

(1) What is the quadrilateral obtained by sequentially connecting the midpoints of the sides of a quadrilateral with equal diagonals?

(2) What is the quadrilateral obtained by connecting the midpoints of each side of a quadrilateral with perpendicular diagonals in sequence?

(3) What is the quadrilateral obtained by sequentially connecting the midpoints of each side of a quadrilateral with equal and perpendicular diagonals?

in conclusion

In fact, the quadrilateral obtained by sequentially connecting the midpoints of each side of the quadrilateral must be a parallelogram, but whether it is a special parallelogram depends on whether its diagonals are perpendicular or equal, and has nothing to do with whether they bisect each other.

Example 2 Known: As shown in the figure, in the quadrilateral ABCD, E, F, G, and H are the midpoints of AB, BC, CD, and DA respectively.

Verify

(1) Quadrilateral EFGH is a parallelogram.

(2) Please add a condition to make the quadrilateral ADFE a rhombus.

(3) Please add a condition to make the quadrilateral ADFE a rectangle.

(4) Can you add just one condition to make the quadrilateral ADFE a square?

Operation:

1.P32 Exercise Question 1, Exercise Question 2 (in the book)

2. Complete the corresponding questions in the exercise book and materials.

Keywords: teaching courseware of the median line theorem of a triangle, Qingdao edition eighth grade mathematics volume PPT courseware download, eighth grade mathematics slide courseware download, download of the median line theorem of a triangle PPT courseware, .PPT format;

For more information about the PPT courseware "The Median Theorem of Triangles", please click on the Median Median Theorem of Triangles PPT tab.

"The Median Line Theorem of Triangles" PPT Courseware 2:

"The Median Line Theorem of Triangles" PPT Courseware 2 A and B are separated by a pond. Now we want to measure the distance between A and B, but we cannot measure it directly. What should we do? In this class, we will explore a measurement method that seems impossible but can be accomplished..

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Update Time: 2024-07-24

This template belongs to Mathematics courseware Qingdao Edition Eighth Grade Mathematics Volume 2 industry PPT template

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