Right-Angled Triangle

A right-angled triangle is a type of triangle that has one angle measuring 90 degrees, which is known as the right angle. The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs. The legs of the right-angled triangle form the right angle, and they can be of different lengths.

Properties of Right-Angled Triangle:

1. The sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse, according to the Pythagorean theorem: a² + b² = c², where a and b are the lengths of the legs, and c is the length of the hypotenuse.

2. The two acute angles of a right-angled triangle are complementary, meaning their measures add up to 90 degrees.

Special Right-Angled Triangles:

There are two special types of right-angled triangles:

1. 45-45-90 triangle: In this type of triangle, the two legs are congruent, and the hypotenuse is the length of the leg multiplied by √2.

2. 30-60-90 triangle: In this type of triangle, the sides are in the ratio 1:√3:2, and it has specific angle measurements of 30, 60, and 90 degrees.

Study Guide:

When studying right-angled triangles, it's important to understand the Pythagorean theorem and how to apply it to find the length of a missing side. Additionally, practice identifying the different types of right-angled triangles and understanding their properties. It's also helpful to be familiar with trigonometric functions such as sine, cosine, and tangent, which are commonly used in right-angled triangle problems.

Practice solving a variety of problems involving right-angled triangles, including finding missing side lengths, calculating angles, and applying trigonometric ratios. Understanding the relationships between the sides and angles of right-angled triangles will be crucial for success in this topic.

Remember to also review the special right-angled triangles and their properties, as they often appear in geometry problems and can simplify calculations.

Finally, make sure to utilize visual aids such as diagrams and geometric figures to help solidify your understanding of right-angled triangles.

Good luck with your studies!