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"Special Parallelogram" PPT Courseware 4
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Definition: A parallelogram with one right angle is called a rectangle.
give it a try
It is known that △ABC is Rt△, ∠ABC=Rt∠, and BD is the midline on the hypotenuse AC
1. If BD=3cm, then AC=________cm
2 If ∠C=30°, AB=5cm, then AC=_______cm,
BD=_______cm, ∠BDC=_______
Do you know how to determine whether a parallelogram is a rectangle?
Definition of rectangle:
A parallelogram with one right angle is a rectangle.
□ABCD
∠A=900
Quadrilateral ABCD is a rectangle
Rectangular determination method 1:
A quadrilateral with three right angles is a rectangle.
Geometry language:
∵ ∠A=∠B=∠C=90°
∴ Quadrilateral ABCD is a rectangle
Rectangular determination method 2:
A parallelogram with equal diagonals is a rectangle.
(A quadrilateral with equal diagonals that bisect each other is a rectangle.)
Geometry language:
∵ Quadrilateral ABCD is a parallelogram
AC=BD
(or OA=OC=OB=OD)
∴ Quadrilateral ABCD is a rectangle
1. Among the following conditions, which one cannot determine that quadrilateral ABCD is a rectangle ( ).
A． AB∥CD, AB=CD, AC=BD
B． ∠A=∠B=∠D=90°
C. AB=BC, AD=CD, and ∠C=90°
D. AB=CD, AD=BC, ∠A=90°
2. Which of the following statements is wrong ( )
A. A parallelogram with one interior angle that is a right angle is a rectangle
B. The four corners of a rectangle are all right angles, and the diagonals are equal
C. A parallelogram with equal diagonals is a rectangle
D. A quadrilateral with two right angles is a rectangle
Summary: How to determine a rectangle
method 1:
A parallelogram with one right angle is a rectangle.
Method 2:
A parallelogram with equal diagonals is a rectangle.
(A quadrilateral with equal diagonals that bisect each other is a rectangle.)
Method 3:
A quadrilateral with three right angles is a rectangle.
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