Special Right Triangles

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Pythagorean Theorem Properties of Special Right Triangles

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Special Right Triangles

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Presentation transcript:

Special Right Triangles 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 ______. BLANK: x(root 2) HONORS: Algebra can be used to verify this conjecture: “make a right triangle with legs length x and hypotenuse c... plug it into the Pythagorean formula and solve for c...

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 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. Blank: x(root 3)

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

Multiples of Right Triangles 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. Cross out existing side lengths and replace with multiples...

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. Writing a Standard Equation of a Circle 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: Writing a Standard Equation of a Circle

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