Isosceles Triangle Study Guide

Definition

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.

Properties

• Two sides of an isosceles triangle are congruent.
• The angles opposite the congruent sides are also congruent.
• The altitude drawn from the vertex angle of an isosceles triangle bisects the base and is also a median and an angle bisector.
• The median drawn from the vertex angle of an isosceles triangle is also an altitude and an angle bisector.

Formulas

For an isosceles triangle with base b and legs a:

• Perimeter = a + a + b = 2a + b
• Area = (1/2) * b * h, where h is the height (altitude) of the triangle
• Height (altitude) can be found using the formula: h = sqrt(a^2 - (b/2)^2)

Example Problems

1. If the legs of an isosceles triangle are each 5 cm long and the base is 6 cm long, what is the perimeter of the triangle?

Perimeter = 2 * 5 cm + 6 cm = 10 cm + 6 cm = 16 cm

2. Find the area of an isosceles triangle with a base of 8 inches and a height of 6 inches.

Area = (1/2) * 8 in * 6 in = 24 square inches

Practice Problems

1. A triangle has two sides of length 9 cm and a base of 12 cm. Find the perimeter of the triangle.

2. An isosceles triangle has a base of 10 meters and a height of 8 meters. Calculate the area of the triangle.

Conclusion

Isosceles triangles have unique properties and formulas that make them an important topic in geometry. Understanding these properties and formulas can help in solving various geometry problems related to isosceles triangles.