"Properties and Judgment of Squares" Special Parallelogram PPT Courseware 4

Description

"Properties and Judgment of Squares" Special Parallelogram PPT Courseware 4

Scenario introduction

Determination theorem for squares:

1. A rhombus with equal diagonals is a square.

2. A rectangle with vertical diagonals is a square.

3. A rhombus with one right angle is a square.

Guess the conclusion, group verification

1. As shown in the figure, in ΔABC, EF is the median line of ΔABC,

①If ∠BEF=30°, then ∠A=_______.

②If EF=8cm, then AC=_______.

2. Find a point D below AC, make the midpoints G and H between CD and AD, and ask what is the relationship between EF and GH? What about EH and FG?

3. What are the characteristics of the shape of the quadrilateral EFGH?

Midpoint quadrilateral of special quadrilateral:

The midpoint quadrilateral of a parallelogram is a parallelogram

The midpoint of a rectangle is a rhombus

The midpoint of a rhombus is a rectangle

The midpoint of a square is a quadrilateral

The midpoint quadrilateral of an isosceles trapezoid is a rhombus

The midpoint quadrilateral of a right-angled trapezoid is a parallelogram

The midpoint quadrilateral of a trapezoid is a parallelogram

question:

1. Rectangle and isosceles trapezoid are quadrilaterals with different shapes. Why do midpoint quadrilaterals change from parallelograms to rhombuses?

2. What conditions need to be added to change a parallelogram into a rhombus?

3. From what perspective do you think about it?

4. Where do you get inspiration from?

5. Can you use your findings to explain other graphical changes? For example: the original quadrilateral is a rhombus, and the midpoint quadrilateral is a rectangle?

Class summary

1. What knowledge is focused on in this lesson, and what mathematical ideas and methods are applied?

2. What did you gain from studying this class? What should we do in the future learning process?

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Update Time: 2024-07-08

This template belongs to Mathematics courseware Beijing Normal University Ninth Grade First Volume Mathematics industry PPT template

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