The property of three medians of a triangle

Welcome to our class Teacher : DO THI HANG Grade : 7A1 Review ……… : Tính chất Triangle: …… … : Kẻ …… : Đoạn thẳng Connect:……… …………: Đỉnh 12 Corresponding:…… 13 ……: Kích thước 14 Intersect at: …… 15 ………: Tỉ số 16 ……….: Định lý 10 11 Point: …… ……… : Đo đạc ….: Quan sát ………: Trung điểm …… : Đường thẳng 17 Pass through :……… 18 …… : giá trị 19 Median :…… 20 The centroid: … 21 ………… : Đồng quy 22 Length:…… Review 12 13 14 15 16 Property : Tính chất Triangle: Tam giác Draw : Kẻ Segment line: Đoạn thẳng Connect: Nối Vertex: Đỉnh Corresponding: Tương ứng Dimension: Kích thước Intersect at: Cắt Ratio: Tỉ số Theorem: Định lý Point: Điểm Measure: Đo đạc Observe: Quan sát 10 Midpoint: Trung điểm 11 Straight line: Đường thẳng 17 18 19 20 21 22 Pass through : Đi qua Values: giá trị Median : Trung tuyến The centroid: Trọng tâm Convergent: Đồng quy Length: Độ dài § Period 53 THE PROPERTY OF THREE MEDIANS OF A TRIANGLE When we say the name of the median, start at the vertex and end at the midpoint A C M B A M B C Sometime the straight line AM is also called the median line of the triangle ABC 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? The properties of three medians of a triangle: a, Practice Step 1: Fold it define the midpoint of a side Step 2: Draw a line connecting a midpoint to its opposite vertex Step 3: Do the same to draw the two other medians Are those three medians meet at one point or not? The three medians of the triangle pass through a point 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 Test : The three points A, G, M are collinear What are the values of the ratios: ; ; Cách hiển thị Menu File: Hiệu chỉnh Phép dựng hình Phép biến hình Đo lường Đồ thị The three points A, G, M are collinear Remark: The medians AM, BE, CF of the triangle ABC pass through the point G • What are the values of the ratios: ; ; We have: = = AG = BG = BE CG = CF c, Theorem 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 The medians AD, BE, CF of the triangle ABC pass through the point G What = =is centroid? The point G is called the centroid of the triangle ABC   d, Identify the centroid How can we find the centroid of a triangle? The first method: Find the intersection of the two median line A F B G The second method: Draw a median and then divide it into equal section The centroid is at the 2/3 length of the median A E G C B D C 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 points on a line + To prove that lines convergent + To calculate the length of the median…… Practice Exercise 1: Fill in the blanks: The median line of a triangle is the line connecting a Vertex …… midpoint of the triangle to the ………………of its opposite side convergent at a point Three medians of a triangle always ……………… The length of the line from a vertex to the centroid is … độ dài of the length of the median from that vertex Practice Exercise Given that G is the centroid of the triangle DEF with the median DH Among the following statements, which one is DG DG GH a,  b,  c,  true? DH GH DH d, GH  DG 20 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? A G B G is the centroid of the triangle C HOMEWORK + Learn by heart the theorems: the medians of a triangle, the properties of three medians of a triangle + Do excersice 24, 25, 26 in text book and 31, 33 in work book THANK YOU FOR ATTENTION ... Theorem 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 The medians AD,... Do the same to draw the two other medians Are those three medians meet at one point or not? The three medians of the triangle pass through a point b, Practice 2: (use Sketchpad)  Draw the triangle. .. end at the midpoint A C M B A M B C Sometime the straight line AM is also called the median line of the triangle ABC AM is the median line of the triangle ABC < = > M is the midpoint of the