JRLeon Geometry Chapter 9.1 HGHS Lesson 9.1 In a right triangle, the side opposite the right angle is called the hypotenuse. The other two sides are called.

Presentación del tema: "JRLeon Geometry Chapter 9.1 HGHS Lesson 9.1 In a right triangle, the side opposite the right angle is called the hypotenuse. The other two sides are called."— Transcripción de la presentación:

1 JRLeon Geometry Chapter 9.1 HGHS Lesson 9.1 In a right triangle, the side opposite the right angle is called the hypotenuse. The other two sides are called legs. In the figure below, a and b represent the lengths of the legs, and c represents the length of the hypotenuse. There is a special relationship between the lengths of the legs and the length of the hypotenuse. This relationship is known today as the Pythagorean Theorem. En un triángulo rectángulo, el lado opuesto al ángulo recto se llama la hipotenusa. Los otros dos lados se llaman catetos. En la figura de abajo, a y b representan la longitudes de los catetos, y c representa la longitud de la hipotenusa. catetos hipotenusa Existe una relación especial entre las longitudes de los catetos y la longitud de la hipotenusa. Esta relación se conoce hoy como el Teorema de Pitágoras

2 JRLeon Geometry Chapter 9.1 HGHS Lesson 9.1 a b c a b c a b c a b c

3 JRLeon Geometry Chapter 9.1 HGHS Lesson 9.1 a b c a b c a b c a b c Area of Large Square is: (c)(c)=c 2 Area del cuadrado grande Length of Small Square = (b – a) Area del cuadrado pequeño This means that the Area of Small Square Esto significa que el área de la = (b – a) 2 So the base (base) = (b – a) and the height (altura) = (b – a) Area of the large square = Area of the small square PLUS the Area of the 4 Triangles Área del cuadrado grande = área del cuadrado pequeño MÁS el área de los 4 triángulos c 2 = a 2 + b 2 Teorema de Pitágoras En todo triángulo rectángulo el cuadrado de la hipotenusa es igual a la suma de los cuadrados de los catetos.triángulo rectángulo hipotenusacatetos

4 JRLeon Geometry Chapter 9.1 HGHS Lesson 9.1 The Pythagorean Theorem works for right triangles, but does it work for all triangles? A quick check demonstrates that it doesn’t hold for other triangles.

5 JRLeon Geometry Chapter 9.1 HGHS Lesson 9.1

6 JRLeon Geometry Chapter 9.2 HGHS Lesson 9.2 Three positive integers that work in the Pythagorean equation are called Pythagorean triples. El inverso del Teorema de Pitágoras Si las longitudes de los tres lados de un triángulo satisfacen la ecuación de Pitágoras, entonces el triángulo es un triángulo rectángulo.

7 JRLeon Geometry Chapter 9.3 HGHS Lesson 9.3

8 JRLeon Geometry Chapter 9.3 HGHS Lesson 9.3 Investigation 1 In this investigation you will simplify radicals to discover a relationship between the length of the legs and the length of the hypotenuse in a 45°-45°-90° triangle. To simplify a square root means to write it as a multiple of a smaller radical without using decimal approximations. Length of each leg1234567...10... l Length of hypotenuse

9 JRLeon Geometry Chapter 9.3 HGHS Lesson 9.3 60° 30° A B C D Given: Equilateral  ABC AC  CB  AB, Equilateral Triangle Definition Construct Perpendicular Angle Bisector CD. AD  BD, Perpendicular Angle Bisector  DCB = 30°, Perpendicular Angle Bisector Let DB = a a 2a Then CB = 2a

10 JRLeon Geometry Chapter 9.3 HQHS Lesson 9.3 Investigation 2 Another special right triangle is a 30°-60°-90° triangle, also called a 30°-60° right triangle, that is formed by bisecting any angle of an equilateral triangle. The 30°-60°-90° triangle also shows up often in mathematics and engineering because it is half of an equilateral triangle. In this investigation you will simplify radicals to discover a relationship between the lengths of the shorter and longer legs in a 30°-60°-90° triangle. Length of shorter leg1234567...10... a Length of hypotenuse2468101214202a Length of longer leg

11 JRLeon Geometry Chapter 9.1-9.2 HGHS Lesson 9.1 / 9.2 Class Work / Home Work: 9.1 Pages 481: problems 1 thru 18 EVEN 9.2 Pages 486-487 : problems 1 thru 18 EVEN 9.3 Pages 493: problems 1 thru 8 ALL