Always, Sometimes , or Never

1. Always, Sometimes, or Never Solve for X Theorems, Definitions Or Postulates One Step Proofs 10 10 10 10 20 20 20 20 30 30 30 30 40 40 40 40 50 50 50 50 Click here for game DIRECTIONS Hardtke Jeopardy Template 2011

2. 10 Always, Sometimes, or Never A triangle with side lengthsof 5, 6 and 8 is obtuse.Click to check answer A(Since 52 + 62 < 82) Click to return to game board

3. 20 Always, Sometimes, or Never If two sides of a right triangle have lengths of 3 cm and 4cm, then the third side has a length of 5cm.Click to check answer S(4 could be the hypotenuse as in a 3cm, cm, 4cm triangle) Click to return to game board

4. 30 Always, Sometimes, or Never If a right triangle contains a 30o angle, then one leg has a length ½ that of the hypotenuse.Click to check answer AAll 30-60-90 ∆s have sides represented by (x, x, 2x) Click to return to game board

5. 40 Always, Sometimes, or Never The sine of an acute angle is equal to the cosine of its complement.Click to check answer A( for one angle will match for the other acute angle) Click to return to game board

6. 50 Always, Sometimes, or Never For some ,sin X = Click to check answer N( Since legs are shorter than hyp, sine and cosine are always less than one.) Click to return to game board

7. 10 Solve for x Click to check answer 3 x 5 4 x = 3x = 16 x = Click to return to game board

8. 20 Solve for x Click to check answer x x 30o 15 long leg = 15 = a short leg = =hyp = Click to return to game board

9. 30 Solve for x Click to check answer x = 2 x2 + 16x – 36 = 0 (x + 18)(x – 2) = 0 Click to return to game board

10. 40 Solve for x If a kite is flying at a vertical height of meters above the ground and the length of string AB is meters, find the horizontal distance CB.Click to check answer = 50 meters (8, 15, 17) multiplied by Click to return to game board

11. 50 Solve for x x is the exact valueof tan 60oClick to check answer 60o Click to return to game board

12. 10 Theorems, Definitions Or Postulates SOHCAHTOA stands for …Click to check answer sin = cos = tan = Click to return to game board

13. 20 Theorems, Definitions Or Postulates Complete the theorem:In a 30-60-90 triangle with hypotenuse of length 2x, then the two legs have lengths of …Click to check answer x and x Click to return to game board

14. 30 Theorems, Definitions Or Postulates Complete the theorem:Given an altitude drawn to the hypotenuse, then either leg of a right triangle is the geometric mean of …Click to check answer the entire hypotenuse and the adjacent segment of the hypotenuse Click to return to game board

15. 40 Theorems, Definitions Or Postulates Write three parts of the Converse of the Pythagorean Theorem.(used to classify triangles)Click to check answer If a2 + b2 = c2, then the ∆ is right. If a2 + b2 < c2, then the ∆ is obtuse. If a2 + b2 > c2, then the ∆ is acute. Click to return to game board

16. 50 Theorems, Definitions Or Postulates The tangent of an acute angle is the _?_ of the tangent of its complement.Click to check answer Reciprocal (since the leg adjacent to one acute angle is opposite from the other acute angle) Click to return to game board

17. 10 One Step Proofs Given: is a right Prove: PR2 + RQ2 = PQ2Click to check answer P Q R Pythagorean Theorem Click to return to game board

18. 20 One Step Proofs Given: PR2 + RQ2 > PQ2Prove: ∆PQR is acuteClick to check answer P Q R Converse of Pythagorean Theorem or if a2 + b2 > c2, then the ∆ is acute Click to return to game board

19. 30 One Step Proofs Given: is a right Prove: cos Q = Click to check answer P Q R Definition of Cosine Or cosine = Click to return to game board

20. 40 One Step Proofs Given: are right sProve: = Click to check answer P S Q R Altitude to the Hypotenuse Theorem or “The altitude to the hypotenuse is the geometric mean of the two segments on the hypotenuse.” Click to return to game board

21. 50 One Step Proofs Given: =90;; PQ =10Prove: RQ = 5Click to check answer P Q R In a 45-45-90 triangle, the hypotenuse is the length of the leg times . Or the sides of a 45-45-90 triangle can be represented by (x, x, x ) Hint: (10 so each leg x is found by = ) Click to return to game board

22. Jeopardy Directions • Any one student may select the first question and students rotate choosing the next question in clockwise order regardless of points scored. • As a question is exposed, EACH student in the group MUST write his solution on paper. (No verbal responses accepted.) • The first student to finish sets down his pencil and announces 15 seconds for others to finish working. • After the 15 seconds has elapsed, check the answer. • IF the first student to finish has the correct answer, he earns the point value of the question and no other students earn points. • IF that student has the wrong answer, he subtracts the point value from his score and EACH of the other students with the correct answer earns/steals the point value of the question. (Those students do NOT lose points if incorrect, only the first student to “ring in” can lose points in this game version.) • Each student should record a running total of his own score. • Good sportsmanship and friendly assistance in explaining solutions is expected! Reviewing geometry is more important than winning. Return to main game board