lesson 10.4 special right triangles. investigation 10.4.2 c-90: isosceles right triangle conjecture...
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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