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"Determination of Parallelograms" Quadrilateral PPT Courseware 4
review review
Definition: A quadrilateral with two sets of opposite sides that are parallel is called a parallelogram.
Property: Opposite sides of a parallelogram are equal;
Opposite angles of a parallelogram are equal.
The diagonals of a parallelogram bisect each other.
Explore: Known: In quadrilateral ABCD, AB=DC, AD=BC. Verify: Quadrilateral ABCD is a parallelogram.
Analysis: To prove that a quadrilateral is a parallelogram, you need to judge based on the definition of a parallelogram, that is, you need to prove that the two opposite sides of the quadrilateral are parallel. From the question, we know that through the congruence of triangles, we can get equal interior angles, and we can prove parallelism.
Proof: Connect AC, in △ABC and △CDA,
AB=CD (known)
AC=CA (common edge)
BC=DA(known)
∴△ABC≌△CDA(SSS)
∴ ∠1=∠4 , ∠ 2=∠3
∴AB∥ CD , AD∥ BC
∴ Quadrilateral ABCD is a parallelogram.
A quadrilateral with two equal sides is a parallelogram.
Similarly, consider the following questions:
When the opposite angles of a quadrilateral are equal, is the quadrilateral a parallelogram?
When the diagonals of a quadrilateral bisect each other, is the quadrilateral a parallelogram?
Determining theorem for parallelograms:
Decision 1 Definition: A quadrilateral with two sets of opposite sides that are parallel is a parallelogram.
Decision 2 A quadrilateral with two sets of opposite sides equal to each other is a parallelogram.
Decision 3 A quadrilateral with two equal opposite angles is a parallelogram.
Decision 4 A quadrilateral with two diagonals bisecting each other is a parallelogram.
1. The ratio of the degrees of ∠A, ∠B, ∠C, and ∠D in the quadrilateral ABCD is given below. Among them, the one that can determine that the quadrilateral ABCD is a parallelogram is ( )
A． 1:2:3:4
B. 2:2:3:3
C. 2:3:2:3
D. 2:3:3:2
2. Among the following conditions, which one can determine that quadrilateral ABCD is a parallelogram ()
A． AB=AD, CB=CD
B. ＡＢ∥ＣＤ，ＡＤ＝ＢＣ
C. AB=CD, AD=BC
D. ∠A＝∠B，∠C＝∠D
induction
We call the line segment connecting the midpoints of the two sides of a triangle the median of the triangle.
From the above question, we can get the triangle median line theorem:
The median of a triangle is parallel to the third side of the triangle and equal to half of the third side.
As shown in the figure above, in △ABC AD=BD, AE=CE
DE∥BC DE=1/2BC
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"Determination of Parallelograms" PPT courseware download:
"Determination of Parallelograms" PPT courseware download Part 1 content: Review Review: Briefly describe the properties of parallelograms: 1. The opposite sides of a parallelogram are equal 2. The diagonals of a parallelogram are equal 3. The diagonals of a parallelogram bisect each other 4. A parallelogram Opposite sides...
"Determination of Parallelograms" PPT download:
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