"Rhombus" PPT courseware

Description

"Rhombus" PPT courseware

Part One: Scenario Creation

We have studied parallelograms and rectangles before, and we know what shape the parallelogram will become if one of its angles is a right angle?

If we specialize the parallelogram from the perspective of the sides, what special quadrilateral will we get?

Activity

In a parallelogram, if the size of the interior angles remains the same and only the lengths of the sides change, please observe and think carefully, what relationships have not changed during this change? What relationships have changed?

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.

Quadrilateral ABCD is a rhombus

Diamond PPT, Part 2: Verification

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

Verify: (1)AB=BC=CD=DA

(2)AC⊥BD

AC bisects ∠DAB and ∠DCB

BD equals ∠ADC and ∠ABC

Prove (1)∵ Quadrilateral ABCD is a rhombus

∴DA=DC (definition of rhombus)

∵DA=BC,AB=DC

∴AB=BC=DC=DA

(2) In △DAC, ∵AO=CO

∴DB⊥AC,

DB splits ∠ADC (three lines into one)

In the same way: DB bisects ∠ABC;

AC bisects ∠DAB and ∠DCB

Rhombus PPT, part 3: properties of rhombus

The two opposite sides of a rhombus are parallel and equal

The four sides of a rhombus are equal

The two opposite angles of a rhombus are equal

The adjacent angles of a rhombus are complementary

The two diagonals of a rhombus bisect each other

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

A rhombus is a centrally symmetrical figure, and the center of symmetry is the intersection of the two diagonals.

A rhombus is an axially symmetrical figure with two axes of symmetry, which are the straight lines where the two diagonals are located.

Diamond PPT, Part 4: Apply what you have learned

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

2. In rhombus ABCD, ∠ABC=60°, 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

Diamond PPT, Part 5: Analysis of Examples

Example 1 As shown in the figure, the perimeter of rhombus ABCD is 16cm.

∠ABC =1200. The diagonals AC and BD intersect at point O. Find the lengths of the diagonals AC and BD of this rhombus.

Solution: ∵AB+BC+CD+AD=16cm

∴AB=BC=CD=AD=4cm

∵BD bisects ∠ABC, ∠ABC=120°

∴ ∠ABD=60°

∴△ABD is an equilateral triangle ∴BD=AB=4cm

Diamond-shaped PPT, part 6: Meeting the standards in class: Show off your skills

1: Distinguish between right and wrong

1. A set of quadrilaterals with equal adjacent sides is a rhombus. ( )

2. A rhombus is a parallelogram. ( )

2. In the rhombus ABCD, O is the intersection point of the two diagonals. It is known that AB=5cm and AO=3cm, then the length of the diagonal AC is ____ and the length of BD is _____.

As shown in the figure, in the rhombus ABCD with side length a, ∠DAB=60 degrees, E is a moving point different from the two points A and D, and F is a moving point on CD, satisfying AE+CF=a.

Prove: No matter how E and F move, triangle BEF is always an equilateral triangle.

Keywords: Free download of Hebei Education Edition mathematics PPT courseware for eighth grade volume 2, diamond-shaped PPT download, .PPT format;

For more information about the "Rhombus" PPT courseware, please click on the Diamond PPT tab.

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Update Time: 2024-07-11

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

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