"Properties of Parallelograms" PPT

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?

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Update Time: 2024-10-05

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