Understanding Isosceles and Equilateral Triangles
Isosceles and equilateral triangles are two special types of triangles that have unique properties. In this guide, we will explore the definitions, properties, and examples of these triangles, as well as provide a worksheet for practice.
What is an Isosceles Triangle?
An isosceles triangle is a triangle with two sides of equal length. The two equal sides are called the legs, and the third side is called the base. The angles opposite the equal sides are also equal.
Properties of Isosceles Triangles:
- Two sides of equal length
- Two equal angles opposite the equal sides
- The altitude to the base is also the angle bisector and the median
What is an Equilateral Triangle?
An equilateral triangle is a triangle with all three sides of equal length. All three angles of an equilateral triangle are also equal, each measuring 60 degrees.
Properties of Equilateral Triangles:
- All three sides of equal length
- All three angles equal, each measuring 60 degrees
- The altitude to any side is also the angle bisector and the median
Key Differences Between Isosceles and Equilateral Triangles
- Isosceles triangles have two equal sides, while equilateral triangles have three equal sides.
- Isosceles triangles have two equal angles, while equilateral triangles have three equal angles.
Examples of Isosceles and Equilateral Triangles
Isosceles Triangle Example:
A triangle with two sides of length 5 cm and one side of length 6 cm is an isosceles triangle.
Equilateral Triangle Example:
A triangle with all three sides of length 4 cm is an equilateral triangle.
Worksheet
Now that we have covered the definitions and properties of isosceles and equilateral triangles, it’s time to practice! Complete the following worksheet to test your understanding.
Section 1: Multiple Choice
- What is the definition of an isosceles triangle? a) A triangle with two sides of equal length b) A triangle with all three sides of equal length c) A triangle with two equal angles d) A triangle with all three angles equal
Answer: a) A triangle with two sides of equal length
- What is the measure of each angle in an equilateral triangle? a) 30 degrees b) 60 degrees c) 90 degrees d) 120 degrees
Answer: b) 60 degrees
Section 2: Short Answer
- What is the name of the line segment that divides an isosceles triangle into two congruent triangles?
Answer: Altitude
- What is the name of the triangle with all three sides of equal length?
Answer: Equilateral triangle
Section 3: Problems
- Draw an isosceles triangle with two sides of length 6 cm and one side of length 8 cm.
- Draw an equilateral triangle with all three sides of length 5 cm.
Section 4: True or False
- All isosceles triangles are also equilateral triangles. (False)
- All equilateral triangles are also isosceles triangles. (True)
📝 Note: Make sure to check your work and show all calculations for problems in Section 3.
What is the main difference between isosceles and equilateral triangles?
+The main difference is that isosceles triangles have two equal sides, while equilateral triangles have three equal sides.
What is the measure of each angle in an equilateral triangle?
+Each angle in an equilateral triangle measures 60 degrees.
Can an isosceles triangle also be an equilateral triangle?
+Yes, if an isosceles triangle has all three sides of equal length, then it is also an equilateral triangle.
In summary, isosceles and equilateral triangles are two special types of triangles with unique properties. Understanding the definitions and properties of these triangles is essential for solving problems and working with triangles in various contexts.
Related Terms:
- Isosceles Triangles Worksheet PDF
- Isosceles and equilateral triangles practice
- Isosceles and equilateral triangles Notes
