"Midline of Triangle" PPT

Description

"Midline of Triangle" PPT

Part One: Knowledge Review

Recall: (1) The midline of a triangle

In a triangle, the line segment connecting a vertex to the midpoint of its opposite side is called the midline of the triangle.

Look at the picture first, then think carefully and answer the questions:

1. Can you define the "median line of a triangle"?

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

2. How many median lines does a triangle have?

3. What is the difference between the median line and the midline of a triangle?

Answer: The median line is the line segment connecting the midpoints of both sides of the triangle;

A midline is a line segment connecting a vertex to the midpoint of its opposite side.

Median line of triangle PPT, part 2 content: hands-on operation

How to cut a triangular piece of paper into two parts so that the two parts can form a parallelogram?

1. Cut a triangle, recorded as △ABC;

2. Take the midpoints D and E of AB and AC respectively, and connect DE;

3. Cut △ABC into two parts along DE, and rotate △ADE 180 degrees around point E to obtain the quadrilateral BCFD.

Discuss

1. Is quadrilateral BCFD a parallelogram? Why?

2. What is the positional and quantitative relationship between DE and BC? Why?

3. In △ABC, D is the midpoint of AB, E is the midpoint of AC, and the line segment DE is the median line of △ABC.

Median line of triangle PPT, part 3: properties of the median line of triangle

Median line theorem of a triangle: The median line of a triangle is parallel to the third side and equal to half of it.

The triangle median theorem has two conclusions:

(1) Indicates the positional relationship--parallel to the third side;

(2) Express the quantitative relationship---equal to half of the third side.

When applying, you need to analyze it in detail and use whichever one you need.

Median line of triangle PPT, part 4 content: problem exploration

Answer the following questions as quickly as possible

Known: As shown in the figure, E and F are the midpoints of AB and AC respectively.

(1)∵ E and F are the midpoints of AB and AC respectively.

∴ EF∥BC (according to the triangle median theorem)

(2) If BC =10cm, then EF =5 �.

(3) If EF =6cm, then BC =12 cm.

[Example] Prove: Connect the midpoints of the four sides of a quadrilateral in sequence, and the resulting quadrilateral is a parallelogram.

It is known that in the quadrilateral ABCD, E, F, G, and H are the midpoints of AB, BC, CD, and DA respectively. Prove: Quadrilateral EFGH is a parallelogram.

Median line of triangle PPT, part 5: summary

1. The median line of a triangle is an important line segment in a triangle and should be distinguished from the midline of the triangle.

2. The triangle median line theorem has two conclusions:

(1) Indicates the positional relationship--parallel to the third side;

(2) Express the quantitative relationship---equal to half of the third side.

When applying, you need to analyze it in detail and use whichever one you need.

3. There are three ways to prove the doubling relationship of line segments:

(1) Triangular median line theorem.

(2) The midline on the hypotenuse of a right triangle is equal to half of the hypotenuse.

(3) The right-angled side opposite to angle 300 of a right triangle is equal to half of the hypotenuse.

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For more information about the "Median Line of Triangle" PPT courseware, please click on the Median Line of Triangle PPT tab.

"Median of a Triangle" Parallelogram PPT:

"The Median Line of a Triangle" Parallelogram PPT, 29 pages in total. Learning objectives: Know the concept of the median line of a triangle, clarify the difference between the median line of a triangle and the median line; understand the median line of a triangle theorem, and be able to use it to carry out relevant demonstrations and calculations. ...

"Median Line of Triangle" PPT download:

"The Median Line of a Triangle" PPT Download Part One Content: Learning Objectives: 1. Explore and master the defining properties of the median line theorem 2. Preliminarily use the triangle median line theorem to solve and reason. Feel the connection between triangles and quadrilaterals, and improve Problem solving skills. ..

"The Median Line of a Triangle" PPT courseware:

"The Median Line of a Triangle" PPT courseware Part One: Learning Objectives: 1. Master the concept of the median line of a triangle and its theorem. 2. Be able to apply the concept and theorem of the median line of a triangle to perform relevant proofs and calculations. 3. Feel the connection between triangles and quadrilaterals, and...

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Update Time: 2024-06-27

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

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