"The Median Line of a Triangle" PPT download

Description

"The Median Line of a Triangle" PPT download

Part One Content: Learning Objectives:

1. Explore and master the defining property theorem of the median line

2. Preliminarily use the triangle median theorem to solve and reason. Feel the connection between triangles and quadrilaterals and improve problem-solving abilities.

Focus: Explore and apply the properties of the median line of a triangle.

Difficulty: Use transformational thinking to solve relevant problems.

Median line of triangle PPT, part 2 content: independent learning in the classroom

Preview exchange: (P66-P68)

1.What is the median line of a triangle? How many medians does a triangle have?

2. What are the properties of the median line of a triangle?

3. How to prove the properties of the median line of a triangle?

Median line of triangle PPT, part 3 content: cooperative exploration

Collaborate to explore the definition of the median line of a triangle (mutual help between teachers and friends)

Hands-on

Cut a triangular piece of paper into a triangular piece of paper and a trapezoidal piece of paper, and assemble the two cut pieces of paper into a parallelogram.

(1) If the two cut pieces of paper can be assembled into a parallelogram, what are the requirements for the position of the cutting marks?

(2) To assemble the two cut pieces of paper into a parallelogram, what kind of graphic transformation can be done to the triangles?

Summary of knowledge points: (Definition of the median line of a triangle)

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

① ∵D ​​and E are the midpoints of AB and AC respectively.

∴ DE is the median line of △ABC

② ∵ DE is the median line of △ABC

∴ D and E are the midpoints of AB and AC respectively.

Collaborate to explore the properties of the median of two triangles (mutual help between teachers and friends)

Guess: In △ABC, what is the positional and quantitative relationship between the median line DE and the side BC?

Is quadrilateral BCFD a parallelogram? Why?

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

Known: In △ABC, AD=DB, AE=EC

Prove: DE∥BC, DE=1/2 BC

Proof: extend DE to F, make EF=DE, connect CF,

∵ ________, ∠AED=∠CEF (the vertex angles are equal), ED=EF

∴△ADE≌△CFE (SAS)

AD=____ (corresponding sides of congruent triangles are equal)

∠ADE=_____ (corresponding angles of congruent triangles are equal)

∴AB∥CF (the internal offset angles are equal and the two straight lines are parallel)

∵AD=DB，∴CF=DB

∴ Quadrilateral BCFD is ________ (a set of quadrilaterals with parallel and equal opposite sides is a parallelogram)

So DF∥BC, DF=BC, that is, _______, DE=1/2 BC.

Median line of triangle PPT, part 4: tracking training

Tracking training one: (mutual check between mentor and friend)

As shown in the figure, two points A and B are blocked by buildings. To measure the distance between two points AB, select a point C on the ground, connect CA and CB, and take the midpoints D and E of CA and CB respectively.

The distance between two points AB can be known from the length of DE.

(1) Do you know the reason?

(2) If the length of DE is 36m, find the distance between points A and B.

Consolidate and improve (mutual help between mentors and friends)

In the quadrilateral lawn ABCD, AD=BC, M is the midpoint of side BC, and N is the midpoint of side BC. There is a movable nozzle P that moves on the diagonal BD. When the nozzle moves to a position on BD, PM and PN are equal. Why?

Keywords: Free download of Hebei Education Edition mathematics PPT courseware for eighth grade volume 2, median line of triangle PPT download, .PPT format;

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

"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...

"Midline of Triangle" PPT:

"The Median Line of a Triangle" PPT Part One Content: Knowledge Review Recall: (1) The median line of a triangle In a triangle, the line segment connecting a vertex and the midpoint of its opposite side is called the median line of the triangle. Look at the picture first, then think carefully and answer the questions: 1. Can you give three...

"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..

File Info

Update Time: 2024-11-05

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

Preview