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"Determination of Parallelograms" Quadrilateral PPT Courseware 3
Properties of parallelograms
Definition: A quadrilateral with two sets of opposite sides that are parallel is a parallelogram.
nature:
1. Opposite sides of a parallelogram are equal, respectively
2. The opposite angles of a parallelogram are equal and the adjacent angles are complementary.
3. The diagonals of a parallelogram bisect each other
Parallelogram Determination Theorem
1. A quadrilateral in which two opposite sides are parallel is a parallelogram.
∵AB∥CD, AD∥BC (known)
∴ Quadrilateral ABCD is a parallelogram
(A quadrilateral with two sets of opposite sides that are parallel is a parallelogram.)
2. A quadrilateral with two sets of opposite sides equal to each other is a parallelogram.
Known: As shown in the figure, in the quadrilateral ABCD, AD=CB, AB=CD
Prove: Quadrilateral ABCD is a parallelogram.
Proof: Link AC
∴ABC ≌△ CDA (SSS)
∴∠1=∠2, ∠3=∠4
∴ AB∥CD, AD∥CB
∴ Quadrilateral ABCD is a parallelogram (parallelogram definition)
True or false question
1. A quadrilateral with three right angles is a parallelogram (√)
2. A quadrilateral with two sets of opposite sides that are equal is a parallelogram (√)
3. A quadrilateral with two equal diagonals is a parallelogram (�)
4. Any quadrilateral with two adjacent angles that are complementary is a parallelogram (√)
5. A quadrilateral with one set of opposite sides parallel and the other set of equal sides must be a parallelogram (�)
6. A quadrilateral with two equal sides and two other equal sides must be a parallelogram (�)
What have you gained from studying this lesson?
1. A quadrilateral with two sets of opposite sides that are parallel is a parallelogram.
∵AB∥CD，AD∥BC
∴ Quadrilateral ABCD is a parallelogram
2. A quadrilateral with two sets of opposite sides equal to each other is a parallelogram.
∵ AD=CB，AB=CD
∴ Quadrilateral ABCD is a parallelogram
3. A quadrilateral with two equal opposite angles is a parallelogram.
∵ ∠BAD= ∠BCD, ∠ABC= ∠ADC
∴ Quadrilateral ABCD is a parallelogram
4. A quadrilateral whose diagonals bisect each other is a parallelogram.
∵ AO=OC，BO=OD
∴ Quadrilateral ABCD is a parallelogram
practice
1. In △ABC, D and E are the midpoints of AB and AC respectively. BC=10cm, then DE=______.
2. In △ABC, D and E are the midpoints of AB and AC respectively, ∠A=50°, ∠B=70°, then ∠AED=_____.
Consolidate after class
1. (Fill in the blank) The perimeter of a triangle is 135cm. If parallel lines are drawn through the vertices of the triangle to the opposite sides, then the perimeter of the triangle composed of these three parallel lines is ______cm.
2. (Fill in the blanks) Known: In △ABC, points D, E, and F are the midpoints of the three sides of △ABC respectively. If the circumference of △DEF is 12cm, then the circumference of △ABC is ______cm.
summary
1. The definition of the median line of a triangle
The line segment connecting the midpoints of both sides of a triangle is called the median of the triangle
2. Triangle median theorem
The median of a triangle is parallel to the third side of the triangle and equal to half of the third side
3. The distance between two parallel lines
The distance from any point on a straight line to another straight line is called the distance between these two parallel lines
The distance between parallel lines is equal everywhere
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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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"Determination of Parallelograms" PPT:
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