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Authoritative PPT Summary
"Rectangle" PPT
Part 1: Recall the properties of parallelograms
A quadrilateral with two opposite sides that are parallel is a parallelogram
Properties of parallelograms:
Opposite sides of a parallelogram are parallel;
Opposite sides of a parallelogram are equal;
The diagonals of a parallelogram bisect each other;
Opposite angles of a parallelogram are equal;
Rectangle PPT, part 2 content: Definition of rectangle:
A parallelogram with one right angle is a rectangle
Symmetry of a rectangle:
It is both an axially symmetrical figure and a centrally symmetrical figure.
Draw a rectangle at will, please explore its symmetry. If it is a centrally symmetrical figure, find its center of symmetry. If it is an axis-symmetrical figure, find its axis of symmetry.
Rectangular PPT, part 3: cooperative learning:
(1) Use the instability of the parallelogram, observe the change process from the parallelogram to the rectangle, and think about which elements have changed and which elements have not changed?
(2) Guess which properties of the sides, interior angles, and diagonals of a rectangle have changed compared to those of a parallelogram, and which have not changed?
Property 1: All four corners of a rectangle are right angles
Property 2: The diagonals of a rectangle are equal;
Known: Quadrilateral ABCD is a rectangle. Prove: AC = BD
Proof: In rectangle ABCD
∠ABC = ∠DCB = 90°
AB = DC, BC = CB
∴△ABC≌△DCB (SAS)
∴AC = BD
Rectangular PPT, Part 4: Use properties to improve abilities
Question 1:
(1) Based on the above properties of rectangles, what relationship can you find between OA, OB, OC, and OD?
(2) From OA=OB=OC=OD, how many isosceles triangles are there in the picture? Are these triangles congruent? Do they have the same areas?
(3) If BC=8 is known and the distance from O to BC is 3, find the area, perimeter and diagonal length of the rectangle.
Question 2: As shown in the figure, the two diagonals of rectangle ABCD intersect at point O
(1) If ∠AOD=120 degrees, try to determine the shape of ΔAOB.
(2) To get that ΔAOB is equilateral Δ, what condition can you add?
(3) If ∠AOD=120 degrees, AB=4 cm, find the diagonal length, perimeter and area of the rectangle.
Rectangular PPT, part 5: give it a try
Quadrilateral ABCD is a rectangle
1. If it is known that AB=8�, AD=6�,
Then AC=_____� OB=_____ �
2. If ∠CAB=40° is known, then ∠OCB=
∠OBA=_____ ∠AOB=_____∠AOD=_____
3. If it is known that AC=10� and BC=6�, then the perimeter of the rectangle=_____ �
Area of rectangle =_____ �2
4 If it is known that ∠DOC=120°, AD=6�, then AC=_____�
Rectangular PPT, Part 6: Take a test
1. Properties that rectangles have but parallelograms don’t ( )
(A) The sum of interior angles is 360 degrees (B) Opposite angles are equal
(C) Opposite sides are parallel and equal (D) Diagonals are equal
2. Among the following properties, a rectangle does not necessarily have ( )
(A) The diagonals are equal (B) The four angles are equal
(C) is an axially symmetrical figure (D) the diagonal is vertical
3. Among the following figures, which one is both an axially symmetrical figure and a centrally symmetrical figure ( )
(A) Angle (B) Any triangle (C) Rectangle (D) Isosceles triangle
4. Draw a perpendicular line from one vertex of the known rectangle to the diagonal line opposite it. The perpendicular line is divided into two parts with a right angle of 3:1. Then the angle between the perpendicular line and the other diagonal line is ( )
(A) 60 degrees (B) 45 degrees (C) 30 degrees (D) 22.5 degrees
Rectangle PPT, part 7: Judgment of rectangle:
1. A parallelogram with one right angle is a rectangle;
2. Determination theorem 1
A parallelogram with equal diagonals is a rectangle.
3. Determination theorem 2
A quadrilateral with three right angles is a rectangle;
Take a test:
Are the following statements about rectangles correct?
(1) A quadrilateral with equal diagonals is a rectangle;
(2) A quadrilateral whose diagonals bisect each other and are equal is a rectangle;
(3) A quadrilateral with one right angle is a rectangle;
(4) A quadrilateral with three equal angles is a rectangle;
(5) A quadrilateral with three right angles is a rectangle;
(6) A quadrilateral with four equal angles is a rectangle;
(7) A quadrilateral with equal diagonals and one right angle is a rectangle;
(8) A set of diagonally complementary parallelograms is a rectangle;
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"Rectangle" PPT courseware download:
Download the first part of "Rectangle" PPT courseware: Review the past and learn new things. A quadrilateral with two sets of opposite sides that are parallel is a parallelogram. Properties of parallelograms: Opposite sides of a parallelogram are parallel; Opposite sides of a parallelogram are equal; Diagonals of a parallelogram are parallel to each other. .