1. Altitude-on-hypotenuse

2. Find the value of x x 4√3 10 x = 4√3 4√3 x + 10 x 2 + 10x = 163 x 2 + 10x – 48 = 0 (x – 4)(x + 12) = 0 x = 4 x = -12

3. Find the value of x x j 9 j = 6 6 j + 9 j 2 + 9x = 36 j 2 + 9x – 36 = 0 (j – 3)(j + 12) = 0 j = 3 j = -12 6 3 = x x 9 x 2 = 27 x = 3√3

4. Find the value of x x 4√3 5√3 4√3 = x x 5√3 x 2 = 203 x 2 = 60 x = 2√15

5. Find the value of x x 3 12 12 = x x 15 x 2 = 180 x = 6√5

6. Find the value of x x 4√5 8 x + 8 = 4√5 4√5 8 8x + 64 = 165 8x + 64 = 80 8x = 16 x = 2

7. Pythagorean Thm and Converse

8. Find the value of x x 4√3 10 10 2 + (4√3) 2 = x 2 100 + 163 = x 2 x 2 = 148 x = 2√37

9. Find the value of x x 26 10 10 2 + x 2 = 26 2 100 + x 2 =676 x 2 = 576 x = 24

10. Do the following sides lengths form an acute, right, or obtuse triangle? 25, 24, 7 7 2 + 24 2 ? 25 2 49 + 576 = 625 right

11. Do the following sides lengths form an acute, right, or obtuse triangle? 12, 13, 15 12 2 + 13 2 ? 15 2 144 + 169 > 225 acute

12. Do the following sides lengths form an acute, right, or obtuse triangle? 32, 35, 64 32 2 + 35 2 ? 64 2 1024 + 1225 < 4096 obtuse

13. Radicals

14. Simplify the radical expression. √200 + √50 + 3 √8 10 √2 + 5 √2 + 32 √2 10 √2 + 5 √2 + 6 √2 21 √2

15. Simplify the radical expression. 4√12 + 5√72 + 8√147 42 √3 + 56 √2 + 87 √3 8√3 + 30√2 + 56√3 30√2 + 64√3

16. Simplify the radical expression. 8 √6 3 √2 10 243 √2 = 72 √2 = 36 √2 10 10 5

17. Simplify the radical expression. √200 5 √3 10 √2 √3 2 √6 = 2 √6 5 √3 √3 5315

18. Simplify the radical expression. 6√5 9√3 2√5 √3 2√15 = 2 √15 3√3 √3 33 9