三角形的基本性質和類型

Problem

Create a video about triangles.

Step 1: Identify the Parts of a Triangle

A triangle is a closed, flat shape made from $3$ straight sides. The $3$ sides meet at $3$ vertices, and each vertex forms an inside angle.

So every triangle has:

• $3$ sides
• $3$ vertices
• $3$ angles

Step 2: Use the Angle Sum Rule

For every triangle, the measures of the $3$ inside angles always add up to $180^\circ$.

If the angles are $A$, $B$, and $C$, then:

$$A + B + C = 180^\circ$$

Step 3: Classify Triangles by Side Lengths

Triangles can be sorted by comparing their side lengths.

A triangle with $3$ equal sides is called an equilateral triangle.

A triangle with exactly $2$ equal sides is called an isosceles triangle.

A triangle with no equal sides is called a scalene triangle.

Step 4: Classify Triangles by Angle Sizes

Triangles can also be sorted by the sizes of their angles.

A triangle with all angles less than $90^\circ$ is called an acute triangle.

A triangle with one $90^\circ$ angle is called a right triangle.

A triangle with one angle greater than $90^\circ$ is called an obtuse triangle.

Step 5: Describe a Triangle Completely

A triangle can often be described in two ways at the same time: by its side lengths and by its angle sizes.

A complete basic description of a triangle includes its $3$ sides, $3$ angles, the angle sum rule

$$A + B + C = 180^\circ,$$

a side-length type, and an angle-size type.