# Proportion in a Right Triangle Worksheets

What Proportions Apply in a Right Triangles? Right triangles are pretty interesting shapes having many intricacies and theorems attached to them. A right triangle consists of three sides like every other form of a triangle. All of these sides are unequal in measurements. The longest of these sides is known as the hypotenuse, and the other two sides are called base and perpendicular. The angle between the base and the perpendicular is ninety degrees, and the sum of the other two angles is collectively equal to ninety degrees. A right triangle can be broken down into proportions by dropping a perpendicular from the vertex that is opposite to the hypotenuse and has an angle of ninety degrees, to the hypotenuse. In this way, we break the right triangle in two smaller right triangles that are proportional to the bigger right triangle in size. Following are the ratios in which these dimensions can be divided: The perpendicular of the bigger right triangle to its base. The larger part of the hypotenuse of the bigger right triangle to the length of the perpendicular drawn internally. The internal perpendicular to the smaller part of the hypotenuse of the larger triangle.

• ### Basic Lesson

Guides students through solving Proportion in a Right Triangle.

• ### Intermediate Lesson

Demonstrates the concept of advanced skill while solving Proportion in a Right Triangle. In right triangle ABC, CD is the altitude to the hypotenuse, AB. The segments of the hypotenuse, AB, are in the ratio of 3:7. The altitude is 8. Find the two segments of the hypotenuse.

• ### Independent Practice 1

A really great activity for allowing students to understand the concepts of the Proportion in a Right Triangle. In right triangle ABC, CD is the altitude to the hypotenuse, AB. The segments of the hypotenuse, AB, are in the ratio of 2:5. The altitude is 8. Find the two segments of the hypotenuse.

• ### Independent Practice 2

Students use Proportion in a Right Triangle in 20 assorted problems. The answers can be found below.

• ### Homework Worksheet

Students are provided with 12 problems to achieve the concepts of Proportion in a Right Triangle.

• ### Skill Quiz

This tests the students ability to understand Proportion in a Right Triangle.

• ### Answer Key

Answers for all lessons and independent practice.

#### Eye Color Problem

If you took 100 people and put them in a room, and 63 had blue eyes, than how many people would have brown eyes?

Answer: most people would say 37 people ( 100 minus 63); however, that answer would be wrong, since the odds are that at least a few of the people remaining would have either green or hazel eyes. The real answer is: between 1 and 37.