1. Special Right Triangles
Lesson 10.4
Special Right Triangles

2. 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...

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

4. Investigation 10.4.4 C-92: 30-60 Right Triangle Conjecture -
In a 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)

5. Special Right Triangles
In general
30-60 Right Triangle
aka Right Triangle
Isosceles Right Triangle

6. Multiples of Right Triangles
Lesson 10.5
Multiples of Right Triangles

7. 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...

8. 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.

9. Lesson 10.7 & 10.8
Distance Formula

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

11. 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.

12. 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

13. 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

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