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"Parallelograms and Their Properties" PPT Courseware 6
1. The concept of parallelogram:
1. Definition: A quadrilateral with two sets of opposite sides that are parallel is called a parallelogram.
2. Characteristics: a. It is a quadrilateral; b. There are two sets of opposite sides that are parallel.
3. Symbol: "□" For example, parallelogram ABCD is recorded as: □ABCD; read as: parallelogram ABCD
4. Relevant names:
(1) Opposite side, (2) Adjacent side;
(3) Opposite angles, (4) Adjacent angles;
(5) High.
Typical examples (1)
1. As shown in the figure: □ABCD, EF∥AB,
①Then there are __parallelograms in the picture;
②If GH∥AD, EF and GH intersect at point O, then there are __parallelograms in the figure.
Discussion
1. What are the properties of the sides of a parallelogram? Tell us your reasons.
2. What are the properties of the angles of a parallelogram? Tell us your reasons.
Properties of parallelograms:
1. Opposite sides of a parallelogram are parallel and equal
2. Opposite angles of a parallelogram are equal.
Properties of parallelograms
Theorem 1: Opposite sides of a parallelogram are equal.
Known: As shown in the figure, quadrilateral ABCD is a parallelogram.
Prove: AB=CD, BC=DA.
Analysis: To prove that AB=CD and BC=DA can be proved by converting the corresponding sides of congruent triangles, auxiliary lines can be drawn to achieve the purpose.
Proof: Connect AC.
∵ Quadrilateral ABCD is a parallelogram,
∴AB∥CD,BC∥DA.
∴∠1=∠2, ∠3=∠4.
In △ABC and △CDA, ∠1=∠2, AC=CA, ∠3=∠4
∴△ABC≌△CDA(ASA).
∴AB=CD,BC=DA.
Property application
Typical examples (2)
A: Basic knowledge:
If ∠A=130°, then ∠B=______, ∠C=______, ∠D=______
B: Variation training:
1. If ∠A+ ∠C= 200°, then ∠A=______, ∠B=______
2. If ∠A:∠B= 5:4, then ∠C=______, ∠D=______
Variation exercises:
As shown in the figure: In □ABCD, ∠A+∠C=200°
Then: ∠A=______, ∠B=______.
Solution: ∵ Quadrilateral ABCD is a parallelogram
And ∠A+∠C=200°
∴∠A=∠C=100 ° (opposite angles of a parallelogram are equal)
Also ∵AD∥BC (opposite sides of a parallelogram are parallel)
∴∠B= 180 °－∠A= 180º－ 100°=80°
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"Parallelograms and Their Properties" PPT courseware 5:
"Parallelograms and Their Properties" PPT Courseware 5 Knowledge Review Definition A quadrilateral with two sets of opposite sides that are parallel is a parallelogram. Properties: Opposite sides of a parallelogram are parallel and equal; Opposite angles of a parallelogram are equal; Adjacent angles are complementary. Caught between two parallel lines...
"Parallelograms and Their Properties" PPT courseware 4:
"Parallelogram and Its Properties" PPT Courseware 4 Review: 1. What is a parallelogram? How to express? 2. What are the properties theorems of parallelograms? 3. How to express its property theorem in geometric language? Experiments and Inquiries Please read Chapter 6 of the textbook carefully.
"Parallelograms and Their Properties" PPT courseware 3:
"Parallelograms and Their Properties" PPT courseware 3 Parallelogram concept: A quadrilateral with two sets of opposite sides that are parallel is called a parallelogram. Opposite sides: AB and CD, AD and BC Opposite angles: DAB and BCD, ABC and CDA Diagonals: AC, BD Mathematical symbols of parallelograms:..