"Special Parallelograms" Quadrilateral PPT Courseware 4

Description

"Special Parallelograms" Quadrilateral PPT Courseware 4

learning target

1. Experience the process of exploring the rhombus property determination theorem;

2. Master the properties and determination methods of rhombus, and cultivate students’ logical reasoning ability and organized expression ability.

Knowledge explanation

If the lengths of the sides are changed so that the two adjacent sides are equal, what kind of quadrilateral will this parallelogram form?

A set of parallelograms with equal adjacent sides is called a rhombus.

A rhombus is a special parallelogram that has all the properties of a parallelogram.

Properties of rhombus Theorem 1: All four sides of a rhombus are equal.

Example questions

Known: As shown in the figure, quadrilateral ABCD is a rhombus.

Prove: AB=BC=CD=DA.

Analysis: Based on the definition of rhombus and the properties of parallelogram, the problem can be proved.

Prove: ∵ Quadrilateral ABCD is a rhombus,

∴AB=AD, quadrilateral ABCD is a parallelogram.

∴AB=CD,AD=BC.

∴ AB=BC=CD=AD.

Track training

1. Commonly used determination methods for diamond shapes:

(1) There is a group of _______ equal _____________ called rhombus.

(2) A parallelogram whose diagonals ______ each other is a rhombus.

(3) A quadrilateral whose diagonals ____________ each other is a rhombus.

(4) A quadrilateral with four sides ______ is a rhombus.

2. The diagonals AC and BD of ABCD intersect at point O,

(1) If AB=AD, then □ABCD is _____ shape;

(2) If AC=BD, then □ABCD is _____ shape;

(3) If ∠ABC is a right angle, then □ABCD is _____ shape;

(4) If ∠BAO=∠DAO, then □ABCD is _____ shape.

Practice in class

1. (2010·Yancheng High School Entrance Examination) As shown in the figure, in the rhombus ABCD, the two diagonals AC=6, BD=8, then the side length of this rhombus is ( )

A. 5B． 6C. 8 D. 10

[Analysis] Choose A. According to the diagonals of the rhombus bisect each other perpendicularly and the Pythagorean theorem, the side length of the rhombus is 5

2. (2010 Xi'an High School Entrance Examination) If the side length of a rhombus is 2, then the sum of the squares of the two diagonals of the rhombus is ( )

A. 16B． 8C. 4D． 1

3． (2010·Nantong High School Entrance Examination) As shown in the figure, in rhombus ABCD, AB = 5, ∠BCD = 120°, then the length of diagonal AC is ______

[Analysis] According to the diagonal of the rhombus bisecting a set of opposite angles, we can get ∠BAC = 60°, and AB=BC, then △ABC is an equilateral triangle, ∴AC=AB=5.

Answer: 5

Summary of this lesson

Through the study of this class, we need to master:

1. Definition: A set of parallelograms with equal adjacent sides is called a rhombus.

2. Theorem of properties of rhombus:

(1) All four sides of a rhombus are equal.

(2) The diagonals of a rhombus are perpendicular to each other, and each diagonal bisects a set of opposite angles.

3. The determination theorem of rhombus:

(1) A quadrilateral with four equal sides is a rhombus.

(2) A parallelogram whose diagonals are perpendicular to each other is a rhombus.

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Update Time: 2024-11-26

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