## Isosceles and Equilateral Triangles Worksheet Answer Key 4-6 Introduction:

Triangles are undoubtedly one of the foundational mathematical principles students learn. There are various types of triangles, but in this blog post, we aim to tackle two critical types: isosceles and equilateral triangles. For students who struggle with solving these types of triangles, we understand your frustration. That’s why we have created a simple guide highlighting the answers for worksheets 4-6, which will enable you to not only solve the problem quickly but also understand how to get the solution. Without further ado, let’s dive into the body of the article.

### Blog Body:

This section explores the various things you need to understand about isosceles and equilateral triangles and how to solve them.

- Isosceles Triangle

An isosceles triangle is a type of triangle where two sides are equal in length. This type of triangle is commonly denoted as a triangle ABC, whereby AB = AC. When solving isosceles triangle problems, the first task is to determine whether the triangle is an isosceles one. Most problems provide this information, but in the absence of such information, look out for two sides whose lengths are the same.

Next, use the Pythagorean Theorem, Law of Cosines, or Law of Sines to determine the third side’s length. If the isosceles triangle problem provides the altitude and the base of the triangle lengths, you can calculate the area of the triangle. The formula for the area of an isosceles triangle is A = b(√a^2−b^2/4)/2.

- Equilateral Triangle

An equilateral triangle is a special type of triangle where all three sides have the same length. It is denoted by a triangle ABC, where AB=BC=AC. To solve an equilateral triangle problem, you need to understand its properties. First, since all sides have the same length, all its angles are equal, another way to say this is that the angles measure 60 degrees, which is an essential property of the equilateral triangle.

The formula for the perimeter of the equilateral triangle is 3s, where s is the length of any of its sides. To calculate the area of an equilateral triangle, you can use the formula A = √3/4s^2.

- Worksheet 4-6 Answer Key

Now that you understand the properties of isosceles and equilateral triangles, it’s time to get down to business and solve the worksheet problems. Here’s the answer key to worksheet 4-6:

Question 1: The base of an isosceles triangle is 20 cm, and the altitude is 18 cm. Find the length of the other sides. Answer: The length of the other sides is 17 cm.

Question 2: The perimeter of an equilateral triangle is 12 cm. What is the length of each side? Answer: Each side is 4 cm.

Question 3: The lengths of two sides of an isosceles triangle are 10 cm and 25 cm. Find the length of the third side. Answer: The length of the third side is 25 cm.

Question 4: The height of an equilateral triangle is 4 cm. Find its area. Answer: The area of the equilateral triangle is 6.928 cm^2.

- Tips for Solving Isosceles and Equilateral Triangles

To become proficient in solving isosceles and equilateral triangles, try to break down the problem into smaller, manageable parts. Secondly, practice solving problems regularly so that you can quickly identify when a triangle is equilateral or isosceles. Ensure you understand the formulas for finding the perimeter, area, and other essential properties of these triangles.

### Conclusion:

Solving isosceles and equilateral triangles may seem tricky and daunting for most students, but with the right approach and tools, you can master them. As we have highlighted in this blog post, the key to solving these types of triangles is understanding their properties, breaking down problems and practicing consistently. If you follow these principles, you’ll quickly ace worksheet 4-6 and any other math problems that come your way. So go out there and conquer these triangles!