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Category | Format | Size |
---|---|---|
Hebei Education Edition Eighth Grade Mathematics Volume 2 | pptx | 6 MB |
Description
"Properties of Parallelograms" PPT
Part One: Knowledge Review
Properties of parallel lines:
It is known that AB//CD, EF crosses AB, CD to E, F
Two straight lines are parallel
Internal angles are equal
Same angles
Interior angles on same side are complementary
teaching objectives
1: What is a parallelogram?
2: What properties do parallelograms have?
3: How to express these properties in symbolic language?
Properties of parallelograms PPT, part 2: problem exploration
Question 1: What is a parallelogram?
A quadrilateral with two sets of opposite sides that are parallel is called a parallelogram.
The line segment connecting two non-adjacent vertices of a parallelogram is called its diagonal.
The quadrilateral ABCD shown in the figure is a parallelogram.
Recorded as: □ABCD
Pronounced as: Parallelogram ABCD
Line segments AC and BD are the diagonals of ABCD.
Question 2: What properties do parallelograms have?
Properties of parallelograms PPT, Part 3: Properties
Property 1 Opposite sides of a parallelogram are parallel.
Property 2 Opposite sides of a parallelogram are equal.
Property 3 The opposite angles of a parallelogram are equal.
Because "Two straight lines are parallel and the interior angles on the same side are complementary."
Therefore: adjacent interior angles of a parallelogram are complementary
And because "the supplementary angles of the same angle are equal"
Therefore: Opposite angles of a parallelogram are equal
Property 4: Opposite angles of a parallelogram are equal.
Properties of parallelograms and their geometric language:
1. Opposite sides of a parallelogram are parallel;
∵ Quadrilateral ABCD is a parallelogram
∴AB∥CD,AD∥BC
2. Opposite sides of a parallelogram are equal;
∵ Quadrilateral ABCD is a parallelogram
∴AB=CD;AD=BC
3. The opposite angles of a parallelogram are equal;
∵ Quadrilateral ABCD is a parallelogram
∴∠A=∠C;∠B=∠D
4. The diagonals of a parallelogram bisect each other;
∵ Quadrilateral ABCD is a parallelogram AC=6
∴OA=OC=3
Properties of parallelograms PPT, part 4: exercises
fill in the blank:
(1) Parallelograms __________ are parallel, __________ are equal, and __________ are equal;
(2) As shown in the figure below, EF∥BC, GH∥AB, EF and GH intersect at point O, then there are a total of __________ parallelograms in the figure.
It is known that in __ABCD, ∠A + ∠C =280°
Find the measures of the remaining two interior angles.
Properties of parallelograms PPT, part 5: analysis of examples
Example: In □ABCD, it is known that ∠A =30°, find the measures of the other three angles.
Because quadrilateral ABCD is a parallelogram
And ∠A =30° (known)
So ∠C= ∠A=30°∠B= ∠D (opposite angles of a parallelogram are equal)
And because AD∥BC (opposite sides of a parallelogram are parallel)
So ∠A + ∠B =180° (two straight lines are parallel, and the interior angles on the same side are complementary)
So ∠B = ∠D = 180°-∠A = 180°- 30°= 150°
Properties of parallelograms PPT, Part 6 content: Class summary:
1. What properties of graphics are studied in this lesson?
2. What is a parallelogram?
3. From the discussion in this lesson, what are the properties of parallelograms?
Keywords: Free download of Hebei Education Edition mathematics PPT courseware for eighth grade volume 2, PPT download of properties of parallelograms, .PPT format;
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Update Time: 2024-10-05
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