##### Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice) In geometry, special right triangles are great to work with because the ratio of their sides will always be the same, making calculations easier. The two special triangles you need to know are the isosceles (or 45-45-90) and 30-60-90 right triangles.

You can use your knowledge of special right triangles to answer the following questions.

## Practice questions

1. The length of the altitude of an equilateral triangle is Find the length of a side of the triangle.

2. In isosceles right Rectangle PLCE, with diagonal drawn forms a 30-degree angle at Find the length of 1. 8

An equilateral triangle is a triangle with three congruent sides and three congruent angles. Each angle therefore measures 60 degrees. When you draw the altitude, it creates two as in the following figure. The pattern of the sides of a is as follows: The altitude is the side opposite the 60-degree angle; therefore, A side of the equilateral triangle is opposite the 90-degree angle, so it's equal to 2x; therefore, a side of the triangle equals 2. The pattern of the sides of an isosceles right triangle is as follows: In this problem, the side opposite the 45-degree angle is therefore, As shown in the figure, diagonal divides this rectangle into two The pattern of the sides of a is as follows: Line segment PE, measuring 24, is the side opposite the 60-degree angle, so it's equal to therefore, Line segment PL is the side opposite the 60-degree angle, so it equals x. Therefore, 