1. BY PETER HALEY, BEN CIMA, JAKE MILLER, AND MARK ANSTEAD The Awesome Presentation

2. Number 4 Find the geometric mean between 3 and 27.

3. Number 5 ABC is a right triangle. Solve for x, y and z. Theorem 8-1: If the altitude of a right triangle is drawn to the hypotenuse, the length of the altitude is the geometric mean between the segments of the hypotenuse

4. Number 6 Find x, the length of the longer base of this trapezoid, with the given altitude of 12. b

5. Number 7

6. Number 8 Theorem 8-6: in a 45-45-90 triangle, the hypotenuse is 1:1: x=6 y=12

7. Number 9 Theorem 8-6: In a 45-45-90 triangle, the hypotenuse is times as long as a leg. Theorem 8-7: In a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is times as long as the shorter leg Find the values of x and y. Y= X= 4√2

8. Number 10 Solve for x, y, and z. Z=4  Drop a perp, z=4 X=z+4 ---------X=10 Y=4  Hypotenuse of a 45-45-90 triangle with a side of 4

9. Number 11 SOHCAHTOA: sine=opp/hypo, cosine=adj/hypo, tangent: opp/adj Find the value of x.

10. Number 12 Find the value of y. A=

11. Number 13 Find y and z. Y=160 (45-45-90 triangle) y+z=160 (30-60-90 triangle)

12. Number 14 To find the distance from point A on the shore of a lake to point B on an island in the lake, surveyors locate point P with. Find AB.

13. Theorems and Postulates 8-1: If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. CCorollary 1- When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric men between the segments of the hypotenuse. CCorollary 2- When the altitude is drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg.

14. 8-2: (Pythagorean Theorem) In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. 8-3: If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. 8-4: If the square of the longest side of a triangle is less than the sum of the squares of the other two sides, then the triangle is an acute triangle. 8-5: If the square of the longest side of a triangle is greater than the sum of the squares of the other two sides, then the triangle is acute.

15. 8-6: (45-45-90 Theorem) In a 45-45-90 triangle, the hypotenuse is times as long as a leg. 8-7: (30-60-90 Theorem) In a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is times as long as the shorter leg.

16. Geometry Rules!