The property of three medians of a triangle

AM is the median line of the triangle ABCM is the midpoint of the segment BC = > < How many medians are there in a triangle?... The properties of three medians of a triangle:a, Practice

Teacher : DO THI HANG

Grade : 7A1

Welcome to our class

10 Mid point: Trung điểm

11 Straight line : Đường thẳng

19 Median : Trung tuyến

20 The centroid: Trọng tâm

21 Convergent : Đồng quy

22 Length: Độ dài

THE PROPERTY OF THREE MEDIANS OF A TRIANGLE

§ 4 Period 53

When we say the name of the median,

start at the vertex and end at the

midpoint

A B

C

M B

AM is the median line of the triangle ABC

M is the midpoint of the segment BC

= >

<

How many medians are there in a

triangle?

2 The properties of three medians of a triangle:

a, Practice 1

Step 1: Fold it do define the midpoint of a side

Step 2: Draw a line connecting a midpoint to its opposite vertex

Step 2: Draw a line connecting a midpoint to its opposite vertex

Step 3: Do the same to draw the two other medians

The three medians of the triangle pass through a point.

Are those three medians meet at one

point or not?

b, Practice 2: (use Sketchpad)

 Draw the triangle ABC

 Draw the medians BE and CF

These two medians intersect at G

 M is the midpont of the segment BC

1 Test : The three points A, G, M are collinear

2 What are the values of the ratios: ; ;

Menu File:

Hiệu chỉnh Đồ thị

Phép biến hình

Đo lường

Cách hiển thị Phép dựng

hình

The three points A, G, M are collinear

Three medians of a triangle are always convergent at a point The distance from that point to each vertex is equal to the length of the median passing through that vertex

c, Theorem

The medians AD, BE, CF of the triangle ABC pass through the point G

= =

The point G is called the

centroid of the triangle ABC. 

What is centroid?

E F

A

The first method:

Find the intersection

of the two median line

How can we find the centroid of a triangle?

Draw a median and then divide it into 3 equal section The centroid is at the 2/3 length of the median

d, Identify the centroid

e, Application:

+ To prove the centroid of a triangle ABC

+ To prove the midpoint of a segment

+ To prove that the straight line going through the centroid is the median

+ To prove 3 points on a line

+ To prove that lines convergent

+ To calculate the length of the median……

Exercise 1 : Fill in the blanks:

1 The median line of a triangle is the line connecting a .……

of the triangle to the ………of its opposite side

2 Three medians of a triangle always ……… at a point

3 The length of the line from a vertex to the centroid is …

độ dài of the length of the median from that vertex

Vertex midpoint

convergent

Practice

Exercise 2

Given that G is the centroid

of the triangle DEF with the

median DH

Among the following

statements, which one is

true?

Practice

GH 1 c,

Games relay

Rules of the game: For drawings Each member of the

team will go to the board and records the ratio between the segments based on the property of three medians of a

triangle in turn which team wrire as many as possible is winner

Where is the location of the point G in the

triangle so that the cardboard triangles is

balanced on a sharp pointed holder?

G is the centroid of the

triangle

A

THANK YOU

FOR ATTENTION