"Parallelograms and Their Properties" PPT Courseware 5

Description

"Parallelograms and Their Properties" PPT Courseware 5

Knowledge review

Definition: A quadrilateral with two sets of opposite sides that are parallel is a parallelogram.

Properties Opposite sides of a parallelogram are parallel and equal;

Opposite angles of a parallelogram are equal; adjacent angles are complementary.

Parallel line segments sandwiched between two parallel lines are equal.

Perpendicular segments sandwiched between two parallel lines are equal.

In addition to these properties, do parallelograms have other properties?

Take a guess:

What is the relationship between the lengths of line segments OA and OC, and OB and OD?

Can you prove your conclusion?

Conclusion: The diagonals of a parallelogram bisect each other.

Known: As shown in the figure: The diagonals AC and BD of ABCD intersect at point O.

Verify: OA=OC, OB=OD.

prove:

∵ Quadrilateral ABCD is a parallelogram,

∴ AD=BC, AD∥BC.

∴ ∠1=∠2, ∠3=∠4.

∴ △AOD≌△COB(ASA).

∴ OA=OC, OB=OD.

practice

1. As shown in the figure, in □ABCD, AC and BD intersect at point O,

(1) If AC=18cm, BD=24cm, then AO=____, BO=____.

And if AB=13 cm, then the perimeter of △COD is ____.

(2) If the perimeter of △AOB is 30cm and AB=12cm, then the sum of diagonals AC and BD is ____.

2. As shown in the figure: In parallelogram ABCD, AC and BD intersect at point O, AB=8, then the length of the following two line segments that can be used as the diagonal length of the parallelogram is ( )

A. 4, 12 B. 6, 8 C. 8, 26 D. 12, 20

3. It is known that O is the intersection point of the two diagonals of □ABCD. If AC=24mm, BD=38mm, BC=28mm, then the circumference of △OBC is _____

Choose one

1. Select: The characteristics that parallelograms have but general quadrilaterals do not have are ()

A. Instability B. Diagonals bisect each other

C. The sum of the interior angles is 360 degrees. D. The sum of the exterior angles is 360 degrees.

2. As shown in the figure, in □ABCD, the diagonals AC and BD intersect at point O, and AC+BD=20. The perimeter of △AOB is equal to 15, then CD=______.

3. As shown in the figure, in the plane rectangular coordinate system, the coordinates of the vertex O�B�D of □OBCD are as shown in the figure, then the coordinates of the vertex C are ( )

A.(3,7) B.(5,3)

C.(7,3) D.(8,2)

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"Parallelograms and Their Properties" PPT courseware 4:

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Update Time: 2024-08-01

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