# Geometry Chapter 9

## 13 terms

### Polygonal region

The union of a polygon and its interior

### Every polygonal region has a positive number called its area such that: 1. congruent triangles have equal areas; 2. the area of a polygonal region is equal to the sum of the areas of its nonoverlapping parts

The Area Postulate

### Postulate (9)

The area of a rectangle is the product of its base and altitude

### Square of its sides

Corollary to Postulate 9: The area of a square is the _______________

### Theorem (38)

The area of a right triangle is half the product of its legs

### Altitude

The distance from the a triangle's vertex to the opposite side, which is a perpendicular line segment; same as height

### Theorem (39)

The area of a triangle is half the product of any base and corresponding altitude

### Triangles with equal bases and equal altitudes have equal areas

Corollary to Theorem 39

### Altitude

The distance between a quadrilateral's parallel sides

### Theorem (40)

The area of a parallelogram is the product of any base and corresponding altitude

### Trapezoid; half; altitude

Theorem 41: The area of a ______ is ____ the product of its _____ and the sum of its bases

### The square of the hypotenuse of a right triangle is equal to the sum of the squares of its legs

The Pythagorean Theorem

### Converse of the Pythagorean Theorem

If the square of one side of a triangle is equal to the sum of the squares of the other two sides, the triangle is a right triangle