Properties of Isosceles Triangles
Grade 7 Geometry — A Complete Guide
📐 Section 1: Introduction & Definitions
1.1 Triangle Classification by Sides
Before diving into isosceles triangles, let's see where they fit among all triangles classified by their sides. Understanding this classification helps us recognize what makes isosceles triangles special.
Triangles can be classified by the number of equal sides they have:
| Type | Sides | Description |
|---|---|---|
| Scalene | 0 equal sides | All three sides have different lengths |
| Isosceles | At least 2 equal sides | Two (or more) sides are equal ⭐ |
| Equilateral | 3 equal sides | All three sides are equal (special isosceles!) |
Key Insight: An equilateral triangle is a special case of an isosceles triangle — any two of its three equal sides can be considered the "legs."
Interactive visualization — available in the full lesson
Interactive visualization — available in the full lesson
1.2 Isosceles Triangle — Definition
Definition: An isosceles triangle is a triangle that has at least two equal sides.
- The two equal sides are called legs.
- The third side is called the base.
1.3 Parts of an Isosceles Triangle
Interactive visualization — available in the full lesson
Notation for △ABC with AB = AC
| 🔵 Legs | $AB$ and $AC$ (the two equal sides) |
| 🟢 Base | $BC$ (the third side) |
| 🔴 Vertex Angle | $\angle A$ (angle between the two legs) |
| 🟠 Base Angles | $\angle B$ and $\angle C$ (angles adjacent to the base) |
| ⭐ Vertex | Point $A$ — where the two equal sides meet |
Remember: The vertex of an isosceles triangle is the point where the two equal sides (legs) meet. The angle at this vertex is the vertex angle, and the side opposite to it is the base.
Interactive visualization — available in the full lesson
1.4 Visual Recognition
An isosceles triangle is often drawn with the base horizontal and the vertex at the top, but orientation doesn't matter. What matters is that two sides are equal. The triangle below can be dragged — notice how the equal sides always determine the structure!
Interactive visualization — available in the full lesson