## Geometry

### Right Triangles and Trig

Similarity and the Pythagorean Theorem are central concepts in trigonometry. In this unit, students investigate a geometric interpretation of the Pythagorean Theorem, patterns with Pythagorean Triples and the side lengths of special right triangles. Students use concepts from Similarity and Proportion to develop the relationship between the altitude to the hypotenuse in a right triangle and the segments formed by the intersection of the altitude on the hypotenuse and to explore the trigonometric ratios in a right triangle.

### Geometry: Right Triangles and Trig Activities

Title Type

#### Pythagorean Relationships

Investigate the triangles that can be formed using one side of three squares to build the triangle.

• 7113

#### Pythagorean Triples

Explore Pythagorean triples by dragging vertices to find whole number Pythagorean triples.

• 6600

#### Area Measures and Right Triangles

Investigate dependent and independent objects when three equilateral triangles are drawn on the sides of a right triangle.

• 6540

#### Exploring the Pythagorean Theorem

Explore the distance formula and Pythagorean theorem and make the connection between the two.

• 6945

#### Altitude to the Hypotenuse

Explore the relationship between the length of the altitude to the hypotenuse in a right triangle and the lengths of the two segments formed when this altitude intersects the hypotenuse.

• 7101

#### Special Right Triangles

Examine two types of special right triangles and determine the predictable relationships between the lengths of their legs and hypotenuse.

• 7075

#### Trig Ratios

Explore the ratios to develop the concept of the trigonometric functions.

• 7728