Lesson 10.4Lesson 10.4Special Right TrianglesSpecial 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 ______.x 2

Investigation 10.4.3

C-91: In a 30-60 right triangle, if the side opposite

the 30 degree angle has length x, then thehypotenuse has the length 2x.

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 2x.x 3

Special Right Triangles

Isosceles Right Triangle

30-60 Right Triangleaka 30-60-90 Right

Triangle

Lesson 10.5Lesson 10.5Multiples of Right TrianglesMultiples 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

Lesson 10.7 & 10.8

Distance FormulaDistance 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

(x−h)2 + (y−k)2 =r2

(x−(−4))2 + (y−(0))2 =(7)2

(x+ 4)2 + (y)2 =49

Writing a Standard Equation of a Circle

• Determine the center and radius of the circle whose equation is:

Center : (3,−6)radius : 9

Determining the Radius of a CircleYou can also use the center and a point on

the circle to determine the radius.Center : (1, 3)

Point on Circle: (4,8)

(x−h)2 + (y−k)2 =r2

(4 −1)2 + (8 −3)2 =r2

32 + 52 =r2

9 + 25 =r2

36 =r2−> r =6