"Properties and Judgment of Rectangles" Special Parallelogram PPT Courseware

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"Properties and Judgment of Rectangles" Special Parallelogram PPT Courseware

In primary school, we had a preliminary understanding of rectangles. Looking at the rectangle in Figure 2-41, is it a parallelogram? What are its characteristics?

I found that the opposite sides of these rectangles are parallel and equal, therefore, they are parallelograms.

All four corners of these quadrilaterals are right angles.

In a parallelogram, as long as one angle is a right angle, then the other three angles are also right angles.

Draw a rectangle ABCD on the paper (as shown in Figure 2-44), cut it out, and how to fold it so that the parts on both sides of the crease overlap each other? How many folding methods are there to meet this requirement? Guess from this: Is the rectangle an axially symmetrical figure? If so, how many axes of symmetry does it have? Is your guess correct?

Since AD∥BC, therefore EF⊥AD. Similarly, straight line EF is the perpendicular bisector of line segment AD.

Therefore, point B and point C are symmetrical about the straight line EF, and point A and point D are symmetrical about the straight line EF. Therefore, under the reflection about the axis of the straight line EF, the image of the rectangle ABCD coincides with itself. Therefore, the rectangle ABCD is an axis-symmetric figure, and the straight line EF is an axis of symmetry of rectangle ABCD.

practise

1. As shown in the figure, in the quadrilateral ABCD, ∠A=∠B=∠C=∠D,

Prove: Quadrilateral ABCD is a rectangle.

Proof: Because in the quadrilateral, ∠A=∠B=∠C=∠D, the sum of the interior angles of the quadrilateral is 360°, so ∠A=∠B=∠C=∠D= 90°, so the quadrilateral ABCD is a rectangle.

(A quadrilateral with three right angles is a rectangle.)

2. As shown in the figure, in □ABCD, diagonals AC and BD intersect at point O, ∠AOB = 60°, AB= 2, AC= 4. Find the area of ​​□ABCD.

In the quadrilateral ABCD, the diagonals AC and BD bisect each other, and the intersection point is O. Without adding any auxiliary lines, to make the quadrilateral ABCD a rectangle, a condition needs to be added. This condition can be AC=BD or ∠ Any angle among ABC, ∠CDA, ∠BAD, and ∠BCD is a right angle.

According to the determination of rectangle, a parallelogram with equal diagonals is a rectangle or a parallelogram with one right angle is a rectangle.

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Update Time: 2024-07-29

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