Unit 6 - Right Triangles

Radical sign aa Radicand Index b Simplifying Radicals 11/12/2015 Algebra Review

Perfect Squares Simplifying Radicals = 10 2 = 11 2 = 12 2 = 13 2 = 14 2 = 15 2 = 2 2 = 3 2 = 4 2 = 5 2 = 6 2 = 7 2 = 8 2 = 11/12/2015 Algebra Review

4 =2 Their square roots 81 =9 100 = = = = = =15 16 =4 25=5 36=6 64 =8 49=7 9 =3 Simplifying Radicals 11/12/2015 Algebra Review

12 Example 1 1. Find the largest perfect square that will  into the radicand evenly. 2. Write the radicand in factored form using the perfect square as a factor. 3. Simplify the perfect square. (Remove it from the radical.) Simplifying Radicals 11/12/2015 Algebra Review

48 Example 2 2. Write the radicand in factored form using the perfect square as a factor. 3. Simplify the perfect square. (Remove it from the radical.) Simplifying Radicals 1. Find the largest perfect square that will  into the radicand evenly. 11/12/2015 Algebra Review

Example 3Example 4363 Example 5 63 Example 6Example Simplifying Radicals 11/12/2015 Algebra Review

Example 8Example Example Example 11Example Simplifying Radicals 11/12/2015 Algebra Review

1. No perfect square radicand 2. No perfect square factor of the radicand 3. No fraction as a radicand 4. No radical in the denominator 5. No unreduced fractions Rules for Simplifying Radicals 11/12/2015 Algebra Review

Geometric Mean x is said to be the geometric mean between aand b if and only if : a x x b = Right Triangles 11/12/2015

Example 1 Find the geometric mean between 4 and 25. xx =25 4 X 2 = 100 X = 100 = is the geometric mean between 4 & 25. Right Triangles 11/12/2015

Example 2 Find the geometric mean between 3 and 6. xx = 6 3 X 2 = 18 X = 18 = 9 · 2 = 3 2 Right Triangles 11/12/2015

Right Triangles 11/12/ Cut an index card along one of its diagonals. 2.On one of the right triangles, draw an altitude from the right angle to the hypotenuse. 3.Cut along the altitude to form two smaller right triangles. You should now have three right triangles. Compare the triangles. What special property do they share? Explain.

part 2 part 1 If the altitude is drawn to the hypotenuse in a right triangle, then the length of the altitude is the geometric mean between the lengths of the parts of the hypotenuse. alt part 1= part 2 Right Triangles 11/12/2015

part 2 part 1 If the altitude is drawn to the hypotenuse in a right triangle, then the length of a leg is the geometric mean between the length of the part of the hypotenuse adjacent to the leg and the length of the hypotenuse. Leg 1 part 1= hyp Leg 2 hypotenuse Leg 1 part 2= hyp Leg 2 alt Right Triangles 11/12/2015

4 3 x z z y Example 3 Find the value of x, y, and z. Right Triangles 11/12/2015

c 2 = 100 The Pythagorean Theorem The square of the length of the hypotenuse in a right triangle is equal to the sum of the squares of the lengths of the legs. c 2 = a 2 + b 2 c 2 = a 2 + b 2 c 2 = c = 100 = 10 c b a 8 6 c 2 = EX. 4 Right Triangles 11/12/2015

c 2 = a 2 + b 2 c 2 = a 2 + b = a = a 2 c b a = a EX. 5 a = 108 a = 108 = 36 · 3 = 36 · 3 = 6 3 Right Triangles 11/12/2015