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"Special Parallelogram" PPT courseware 3
Review questions
1.What is a parallelogram?
2. What is the relationship between parallelograms and quadrilaterals?
3. What are the properties of parallelograms?
① Sides: Opposite sides are parallel and equal.
②Angles: Opposite angles are equal and adjacent angles are complementary.
③Diagonals: bisect each other.
Read pages 17 to 19 of the text and think about the following questions:
1. What is a rectangle?
2. What are the properties, theorems and corollaries of rectangles?
3. What are the determination theorems for rectangles?
1. Rectangle:
A parallelogram whose interior angles are right angles is called a rectangle.
2. Properties of rectangle:
Properties of Rectangle Theorem 1: The four corners of a rectangle are right angles.
Properties of Rectangle Theorem 2: The two diagonals of a rectangle are equal.
Corollary of the property theorem: The midline of the hypotenuse of a right triangle is equal to half the length of the hypotenuse.
think about it
1. Properties that rectangles have but parallelograms don’t ( )
(A) The sum of interior angles is 360 degrees
(B) Diagonals are equal
(C) Opposite sides are parallel and equal
(D) Diagonals are equal
2. The property that a rectangle does not necessarily have is ( )
(A) Diagonals are equal
(B) The four angles are equal
(C) is an axis-symmetric figure
(D) Diagonal vertical
Class summary
main content:
1. Definition of rectangle: A parallelogram with one right angle is called a rectangle
2. Properties of rectangle:
Opposite sides of a rectangle are parallel and equal.
The four corners of a rectangle are right angles.
The two diagonals of a rectangle are equal and bisect each other.
A rectangle is an axially symmetrical figure.
The midline of the hypotenuse of a right triangle is equal to half the length of the hypotenuse.
Practice in class
It is known that the two diagonals AC and BD of □ABCD intersect at point O, and △AOB is an equilateral triangle. Find the degree of ∠BAD.
Solution: As shown in the figure, △AOB is an equilateral triangle.
So OA=OB.
∵□The diagonals of ABCD bisect each other,
∴AC=2AO,BD=2BO.
∴AC=BD
Therefore □ABCD is a rectangle.
∴ ∠BAD=90°.
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