Lesson 10 4 Special Right Triangles Investigation 10

Lesson 10. 4 Special Right Triangles

Investigation 10. 4. 2 C-90: Isosceles Right Triangle Conjecture In an isosceles right triangle, if the legs have the length of x, then the hypotenuse has the length of ______.

Investigation 10. 4. 3 C-91: In a 30 -60 right triangle, if the side opposite the 30 degree angle has length x, then the hypotenuse has the length 2 x.

Investigation 10. 4. 4 C-92: 30 -60 Right Triangle Conjecture In a 30 -60 right triangle, if the shorter leg has length x, then the longer leg has length _____ and the hypotenuse has length 2 x.

Special Right Triangles Isosceles Right Triangle 30 -60 Right Triangle aka 30 -60 -90 Right Triangle

Lesson 10. 5 Multiples of Right Triangles

Multiples of Pythagorean Triples C-93: Pythagorean Triples If you multiply the lengths of all three sides of any right triangle by the same number, the resulting triangle will also be a right triangle.

Pythagorean Triples. . . C-94: If the lengths of the two sides of a right triangle have a common factor, then the third side also has that factor.

Lesson 10. 7 & 10. 8 Distance Formula

Finding the Distance between two points • Use the Pythagorean Theorem to find the distance between the two points.

Equation of a Circle The standard equation of a line is shown at right where r is the radius and h is the x-coordinate and k is the y-coordinate.

Writing a Standard Equation of a Circle • Write the standard equation of a circle with center (-4, 0) and radius 7. • Step 1: Plug in values • Step 2: Simplify

Writing a Standard Equation of a Circle • Determine the center and radius of the circle whose equation is:

Determining the Radius of a Circle You can also use the center and a point on the circle to determine the radius.