Isosceles Triangle

An isosceles triangle is a triangle that has two sides of equal length. These two equal sides are called the legs, and the third side is called the base. The angles opposite the legs are also equal to each other and are called the base angles.

Properties of Isosceles Triangle:

1. Two equal sides: In an isosceles triangle, two sides are of equal length.
2. Two equal angles: The angles opposite the equal sides are equal to each other.
3. Unequal side and angles: The side opposite the unequal angle is called the base, and the angle opposite the base is called the vertex angle.
4. Median: The median from the vertex angle of an isosceles triangle divides the base into two equal parts.
5. Altitude: The altitude from the vertex angle of an isosceles triangle bisects the base and is also a perpendicular bisector.

Formulas for Isosceles Triangle:

Here are some important formulas related to isosceles triangles:

• Area: The area of an isosceles triangle can be found using the formula: Area = 0.5 * base * height.
• Perimeter: The perimeter of an isosceles triangle can be found by adding the lengths of all three sides together.
• Base Angles: The measure of each base angle in an isosceles triangle can be found using the formula: Base Angle = (180° - Vertex Angle) / 2.

Example Problem:

Find the area of an isosceles triangle with a base of 8 cm and a height of 10 cm.

Solution:

Using the area formula for a triangle, we have: Area = 0.5 * 8 cm * 10 cm = 40 cm².

So, the area of the isosceles triangle is 40 square centimeters.

Study Tips:

When working with isosceles triangles, it's important to remember the properties and formulas associated with this triangle. Here are some study tips:

• Memorize the properties of an isosceles triangle, including the relationship between its sides and angles.
• Practice using the formulas for area, perimeter, and base angles of an isosceles triangle.
• Work through example problems to understand how to apply the properties and formulas in different situations.
• Use diagrams and visualization to help understand the concepts related to isosceles triangles.

By understanding the properties and formulas for isosceles triangles and practicing with different problems, you can build a strong foundation in geometry.