Always, Sometimes , or Never

Always,Sometimes,

or Never

Solvefor X

Theorems, Definitions

Or Postulates

OneStep

Proofs

10

20

30

40

50

10

20

30

40

50

10

20

30

40

50

10

20

30

40

50Hardtke Jeopardy Template 2011Click here for game DIRECTIONS

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

10 Always, Sometimes, or Never

If two sides of a right triangle have lengths of 3 cm and 4 cm, then the

third side has a length of 5 cm.Click to check answer

S (4 could be the hypotenuse as in a 3cm, cm, 4cm triangle)



If a right triangle contains a 30o angle, then one leg has a length

½ that of the hypotenuse.Click to check answer

A All 30-60-90 ∆s have sides represented by (x, x, 2x)



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)



For some , sin X = Click to check answer

N ( Since legs are shorter than hyp, sine and cosine

are always less than one.)




10 Solve for x

5x

3

x = 3x = 16 x =


4


20 Solve for x

15

x

x30o

long leg = 15 = a short leg = =hyp =


5√3


x = 2

x2 + 16x – 36 = 0 (x + 18)(x – 2) = 0Click to return to game board

30 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.


= 50 meters (8, 15, 17) multiplied by


40 Solve for x

𝐴

𝐶 𝐵

x is the exact valueof tan 60o


50 Solve for x


60o

𝑥√3

𝑥 2 𝑥

SOHCAHTOA stands for …


sin = cos = tan = Click to return to game board

10 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 …


x and xClick to return to game board


Complete the theorem:Given an altitude drawn to the

hypotenuse, then either leg of a right triangle is the geometric mean of …


the entire hypotenuse and the adjacent segment of the hypotenuse



Write three parts of the Converse of the Pythagorean Theorem.

(used to classify triangles)


If a2 + b2 = c2, then the ∆ is right.If a2 + b2 < c2, then the ∆ is obtuse.If a2 + b2 > c2, then the ∆ is acute.



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)



Given: is a right Prove: PR2 + RQ2 = PQ2


Pythagorean TheoremClick to return to game board

10 One Step Proofs

R Q

P

Given: PR2 + RQ2 > PQ2

Prove: ∆PQR is acute


Converse of Pythagorean Theorem

or if a2 + b2 > c2, then the ∆ is acuteClick to return to game board

20 One Step Proofs

R Q

P

Given: is a right Prove: cos Q =


Definition of CosineOr cosine =


30 One Step Proofs

R Q

P

Given: are right sProve: =


Altitude to the Hypotenuse Theorem

or “The altitude to the hypotenuse is the geometric mean of the two segments on the hypotenuse.”


40 One Step Proofs

QR

P S

Given: =90;; PQ =10

Prove: RQ = 5Click to check answer

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 = )


50 One Step Proofs

R Q

P

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

Documents

Always, Sometimes , or Never