"Special Parallelogram" PPT courseware 6

Description

"Special Parallelogram" PPT courseware 6

Create scenario one

A square is a special rhombus

Scenario 2

question:

1. When the CD in the picture is moving, what kind of shape does this shape always look like?

2. When CD moves to the CD position and AD=AB, is the quadrilateral ABCD still a rectangle?

A square is a special rectangle

Define a square

Definition: A set of parallelograms with equal adjacent sides and one right angle is called a square

A rhombus with one right angle is a square

A set of rectangles with equal adjacent sides is a square

A square is a special parallelogram, a special rectangle, and a special rhombus.

A square is a perfect shape

symmetry

Axisymmetric graphics

nature

(1) It has all the properties of a parallelogram

Two sets of opposite sides are parallel and equal, two sets of opposite angles are equal, and the diagonals bisect each other.

(2) Has all the properties of a rectangle

The four angles are all right angles and the diagonals are equal

(3) Has all the properties of a rhombus

Four sides are equal; diagonals are perpendicular to each other, and each diagonal bisects a set of opposite angles

Choose one

1. The property that a square has but not necessarily a rectangle is ()

A. The four angles are equal.

B. The diagonals bisect each other perpendicularly.

C. Diagonals are complementary.

D. The diagonals are equal.

2. Properties that squares have but rhombuses don’t necessarily have ( )

A. All four sides are equal.

B. The diagonals bisect each other perpendicularly.

C. A diagonal bisects a set of opposite angles.

D. The diagonals are equal.

Known: As shown in the figure, in square ABCD, point E is on AC.

Prove: BE=DE

Prove: ∵ Quadrilateral ABCD is a square,

∴AB=AD, ∠BAC=∠DAC.

(All four sides of a square are equal, and each diagonal bisects a set of opposite angles)

In △ABC and △ADC

AB=AD

∠BAC=∠DAC.

AE=AE

∴△ABC≌△ADC (SAS)

∴BE=DE (corresponding sides of congruent triangles are equal)

Time-limited homework

1. As shown in the figure, the quadrilateral ABCD is a square. Extend BC to E so that CE=AC. Connect AE. Intersect CD at F. Find the degree of ∠AFC.

2. In the known square ABCD, AC=10, P is a point on AB, PE⊥AC is at E, and PF⊥BD is at F, then PE+PF=______________.

3. Draw an equal side △DCE from the side DC of the square ABCD, then ∠AEB=_____.

4. In square ABCD, M is the midpoint of AD, ME⊥BD is at E, MF⊥AC is at F. If ME+MF =8cm, then AC=________.

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Update Time: 2024-09-11

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