"Triangle" PPT courseware

Description

"Triangle" PPT courseware

Self-learning

By carefully previewing, can you answer the following questions?

1. What is the definition of triangle?

2. What is the composition of a triangle?

3. How to represent a triangle and its sides?

4. How to classify triangles?

1. Definition of triangle

A figure composed of three line segments that are not on the same straight line and are connected end to end is called a triangle.

2. The composition of triangles

Three sides: AB, BC, AC

Three vertices: A, B, C

Three interior angles: ∠A, ∠B, ∠C

The angle formed by two adjacent sides is called the interior angle of a triangle, or simply the angle of a triangle.

3. How to represent a triangle and its sides?

Marked as "△ABC", pronounced as "Triangle ABC"

Sides: AB, BC, AC or a, b, c

Can you classify triangles appropriately?

Divided by sides: A triangle with three equal sides is called an equilateral triangle

A triangle with two equal sides is called an isosceles triangle

A triangle with three sides that are not equal is called a scalene triangle

Cooperation and exchange

isosceles triangle

Both sides that are equal are called waist

The other side is called the bottom

The angle between the two waists is called the vertex angle

The angle between the waist and the bottom is called the bottom angle

Case Analysis

Use a piece of thin wire 18 cm long to form an isosceles triangle.

①If the waist length is twice as long as the bottom side, what is the length of each side?

② Can it form an isosceles triangle with one side 4 cm long?

Solution: ① Assume the length of the base is x cm, then the length of the waist is 2x cm

x+2x+2x=18

Solve to get x=3.6

∴The lengths of the three sides are 3.6 cm, 7.2 cm, and 7.2 cm respectively.

② Can it form an isosceles triangle with one side 4 cm long?

Solution: When the length of 4 cm is the base, let the waist length be x cm,

Then 4+2x=18, the solution is x=7.

∴The lengths of the three sides of an isosceles triangle are 7cm, 7cm, and 4cm.

When the length of 4 cm is the waist length, and the length of the bottom side is x cm, we can get

4×2+x=18, the solution is x=10,

∵4+4�10

∴A triangle cannot be formed at this time

consolidate and improve

A triangle has two equal sides, the perimeter is 20cm, and the length of one side of the triangle is 6cm. What are the lengths of the other two sides?

Solution: When the 6cm long side is the base, let the waist length of the triangle be x

Then 6+2x=20 and the solution is x=7

∴The length of the other two sides is 7cm

When the 6cm long side is the waist length, let the base of the triangle be x

Then x+6×2=20 and the solution is x=8

∴The other two sides are 8cm and 6cm long

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Update Time: 2024-10-03

This template belongs to Mathematics courseware Qingdao Edition Seventh Grade Mathematics Volume 2 industry PPT template

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