"Properties and Judgment of Rhombus" Special Parallelogram PPT Courseware

Description

"Properties and Judgment of Rhombus" Special Parallelogram PPT Courseware

Scenario creation

We learned about parallelograms earlier. If we specialize the parallelogram from the perspective of the sides and make a set of its adjacent sides equal, what special quadrilateral will we get?

think about it

A rhombus is a special parallelogram that has all the properties of a general parallelogram. Can you list some such properties?

The opposite sides of a rhombus are parallel and equal, the opposite angles are equal, and the diagonals bisect each other.

What other special properties does the rhombus have? In this section, you are invited to communicate and explore with your peers.

Ask students to fold a piece of diamond-shaped paper and answer the following questions:

(1) The observed rhombus, is it a centrally symmetrical figure?

(2) Is it an axially symmetrical figure? If so, how many axes of symmetry are there? What is the positional relationship between the axes of symmetry?

(1) The rhombus is a centrally symmetrical figure, and the center is the intersection of the diagonals.

(2) A rhombus is an axially symmetrical figure with two axes of symmetry. They are the straight lines where the two diagonals of the rhombus are located. The two axes of symmetry are perpendicular to each other.

Properties of rhombus:

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

Since the opposite sides of a parallelogram are equal, the opposite sides of a rhombus are equal, and since the adjacent sides are equal, all four sides are equal.

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

Property 2 of a rhombus: The two diagonals of a rhombus bisect each other perpendicularly, and each diagonal bisects a set of opposite angles.

It is known that quadrilateral ABCD is a rhombus

Equal line segments: AB=CD=AD=BC OA=OC OB=OD

Congruent angles: ∠DAB=∠BCD ∠ABC =∠CDA

∠AOB=∠DOC=∠AOD=∠BOC =90°

∠1=∠2=∠3=∠4 ∠5=∠6=∠7=∠8

Isosceles triangle: △ABC △DBC △ACD △ABD

Right triangle: Rt△AOB Rt△BOC Rt△COD Rt△DOA

Congruent triangles: Rt△AOB ≌ Rt△BOC≌ Rt△COD ≌ Rt△DOA

△ABD≌△BCD △ABC≌△ACD

Apply what you learn

1. It is known that the circumference of the rhombus is 12cm, then its side length is ______.

2. In rhombus ABCD, ∠ABC=60 degrees, then ∠BAC=_______.

3. The two diagonal lengths of the rhombus are 6cm and 8cm respectively, then the side length of the rhombus is ( )

A.10cm B.7cm C. 5cm D.4cm

4. In rhombus ABCD, AE⊥BC, AF⊥CD, E and F are the midpoints of BC and CD respectively, then the degree of ∠EAF is ( )

A.75°B.60°C.45°D.30°

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For more information about the PPT courseware "Special Parallelograms and Rhombuses' Properties and Determinations", please click on the Special Parallelograms ppt Properties and Determinations of Rhombuses ppt tag.

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Update Time: 2024-07-28

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