"Properties of Parallelograms" PPT download

Description

"Properties of Parallelograms" PPT download

Part One: Introduction of New Course

Re-recognition of quadrilaterals

Definition: 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.

display method

As shown in the figure above, parallelogram ABCD is recorded as "□ABCD" and pronounced as "parallelogram ABCD", in which line segments AC and BD are called diagonals.

Re-recognition of parallelograms

Observing this parallelogram, apart from "the two sets of opposite sides are parallel respectively", is there any relationship between its sides, angles and diagonals?

Properties of parallelograms PPT, Part 2: Classroom exercises

1. As shown in the figure, in □ABCD, ∠B=50°

Then ∠A=? ∠C=? ∠D=?

2. As shown in the figure, in □ABCD, BC=7, BD=10, AC=6, and the perimeter of △AOD is ______.

3. In □ABCD, ∠A=3∠B, find the degrees of ∠C and ∠D.

Solution: ∵ in □ABCD, AD∥BC

∴∠A+∠B= 180°

It is also known that ∠A=3∠B

Then 3∠B +∠B= 180°

Solution: ∠B= 45°, ∠A=3×45°=135 °

So ∠C=∠A=135 °, ∠D=∠B= 45°

4. It is known that the perimeter of parallelogram ABCD is 60cm, and the length ratio of the two adjacent sides AB and BC is 3:2. Find the lengths of AB and BC.

Solution: ∵In □ABCD, the opposite sides are equal,

And the perimeter of ∵□ABCD is 60cm.

∴AB + BC=30cm.

And AB: BC=3:2, that is, AB=1.5BC.

Then 1.5BC + BC=30, the solution is BC=12 (cm).

And AB=1.5×12=18 (cm).

Properties of parallelograms PPT, part three: summary of this lesson

definition

A quadrilateral with two sets of opposite sides that are parallel is called a parallelogram. The line segment formed by two non-adjacent vertices is called its diagonal.

display method

Parallelogram ABCD, recorded as "□ABCD", pronounced as "parallelogram ABCD", in which line segments AC and BD are called diagonals.

nature

The opposite sides of a parallelogram are equal, the opposite angles are equal, the adjacent angles are complementary, and the diagonals bisect each other, making it a centrally symmetrical figure.

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Update Time: 2024-07-26

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