Read the Rules of the Game Geometry Quiz Read the Rules of the Game Trigonometry Super Bonus Round Tricky Triangles Theorems Symmetry Coordinate Geometry 10 Points 100 A 10 Points 10 Points 10 Points 10 Points 20 Points 20 Points 100 B 20 Points 20 Points 20 Points 30 Points 30 Points 100 C 30 Points 30 Points 30 Points 40 Points 40 Points 40 Points 40 Points 40 Points 100 D 50 Points 50 Points 50 Points 50 Points 50 Points 100 E

How many degrees in a Straight Angle? 10 Points ? See Answer Back to quiz

How many degrees in a Straight Angle? 10 Points 180 There are 180 degrees in a Straight Angle (Axiom 3) Back to quiz

Q1. Find the value of the missing angle in the shape below 10 Points See Answer ? Back to quiz

Q1. Find the value of the missing angle in the shape below 10 Points 44o Theorem : The angles in any triangle add to 180° 50 + 86 + ? = 180 136 + ? = 180 ? = 180 – 136 = 44 Back to quiz

Q2. The triangle below is isosceles.. Why? 20 Points See Answer Back to quiz

Q2. The triangle below is isosceles. Why? 20 Points Theorem : In an isosceles triangle the angles opposite the equal sides are equal. Back to quiz

Q3. What is the missing angle? 30 Points ? See Answer Back to quiz

Q3. What is the missing angle? 30 Points 150o There are at least 2 ways you can get the answer; 2. Theorem 6: Each exterior angle of a triangle is equal to the sum of the interior opposite angles. 100o + 50o = 150o Axiom 3: The number of degrees in a straight angle = 180o 30o + ? = 180 ? = 180o-30o =150o Back to quiz

Q4. Find the missing length? 40 Points ? See Answer Back to quiz

= ? So , 5 = the missing length Q4. Find the missing length 40 Points [Theorem of Pythagoras] In a right-angled triangle the square of the hypotenuse is the sum of the squares of the other two sides. 32+42 = ?2 9 + 16 = ?2 25 = ?2 = ? So , 5 = the missing length Back to quiz

Q5. Are the triangles below, congruent, similar, totally different? Give a reason for your answer 50 Points See Answer Back to quiz

Q5. These triangles are “Similar” 50 Points Theorem: If two triangles are similar, then their sides are proportional, in order. Back to quiz

Q1. Find the missing angle. Give a reason for your answer. 10 Points See Answer Back to quiz

Q1. Find the missing Angle. Give a reason for your answer 10 Points 95o Theorem: Vertically opposite angles are equal in measure. Back to quiz

Q2. Find the missing length in the parallelogram below Q2. Find the missing length in the parallelogram below. Give a reason for your answer. 20 Points ? See Answer Back to quiz

Q2. Find the missing length in the parallelogram below. Give a reason for your answer. 3 20 Points Theorem: The diagonals of a parallelogram bisect each other. Back to quiz

Q3. Are the lines |a| and |b| below parallel Q3. Are the lines |a| and |b| below parallel? Give a reason for your answer 30 Points See Answer Back to quiz

Angles are NOT the same size Q3. Are the lines |a| and |b| below parallel? Give a reason for your answer Angles are NOT the same size 30 Points No the lines are NOT parallel Theorem 5 (Corresponding Angles). Two lines are parallel if and only if for any transversal, corresponding angles are equal. Back to quiz

Q4. Give 2 reasons why you can be sure the shape below is a parallelogram 40 Points See Answer Back to quiz

Q4. 2 reasons why we can be sure this shape is a parallelogram. Opposite sides are equal in length 40 Points Opposite angles are equal in measure Back to quiz Theorem: In a parallelogram, opposite sides are equal and opposite angles are equal.

Q5. Find the values of x and y below. What theorem supports you answer? 50 Points X See Answer Y Back to quiz

Q5. Find the values of x and y below. What theorem supports you answer? 50 Points Theorem: Let ABC be a triangle. If a line l is parallel to BC and cuts [AB] in the ratio s:t, then it also cuts [AC] in the same ratio. Back to quiz

Q1. Copy the shape and draw in the axis of symmetry 10 Points See Answer Back to quiz

Q1. Copy the shape and draw in the axis of symmetry 10 Points 1 Axis of symmetry Back to quiz

Q2. How many axes of symmetry does this shape have? 20 Points See Answer Back to quiz

Q2. How many axes of symmetry does this shape have? 20 Points 2 Axis of symmetry Back to quiz

T Q3. Copy this shape and draw its reflection through the given line 30 Points T Line of Reflection See Answer Back to quiz

T T Q3. Copy this shape and draw its reflection through the given line 30 Points T T Line of Reflection Back to quiz

E Q4. Copy this shape and draw its reflection through the given line 40 Points E Line of Reflection See Answer Back to quiz

E E Q4. Copy this shape and draw its reflection through the given line 50 Points E E Line of Reflection Back to quiz

Q5. Copy this shape and draw its reflection through the Point D 50 Points A B C See Answer Back to quiz

Q5. Copy this shape and draw its reflection through the Point D 50 Points A B C Back to quiz

Q1. Name the points A and B 10 Points Y Axis 3 A 2 1 X Axis -3 -2 -1 1 -3 -2 -1 1 2 3 -1 B See Answer -2 Back to quiz -3

Q1. Name the points A and B 10 Points (-3, 2) (2, -2) 3 A 2 1 -3 -2 -1 -3 -2 -1 1 2 3 -1 B -2 (2, -2) Back to quiz -3

Q2. Find the distance between Scooby and his snacks. 20 Points Y Axis 15 10 (-10, 10) 5 X Axis -15 -10 -5 5 10 15 -5 See Answer -10 (15,-10) Back to quiz -15

Q2. Find the distance between Scooby and his snacks. 20 Points Y Axis Yummy! 15 10 (-10, 10) 5 X Axis -15 -10 -5 5 10 15 -5 Scooby must walk 32units to get his yummy snacks! -10 (15,-10) -15 Back to quiz

Mmm.. Where should I cut this chain? Q3. A jeweller needs to cut this gold chain exactly in half, at what point should he make the cut? 30 Points Y Axis (4,6) 6 Mmm.. Where should I cut this chain? 4 2 X Axis 2 4 6 -6 -4 -2 -2 See Answer -4 Back to quiz -6 (-6,-6)

Q3. A jeweller needs to cut this gold chain exactly in half, at what point should he make the cut? 30 Points Find the Mid Point Y Axis (4,6) 6 4 2 (-1,0) X Axis 2 4 6 -6 -4 -2 -2 -4 Back to quiz -6 (-6,-6)

Think.. What do you know about perpendicular slopes? Q4. Look at the picture below, how can you know for a fact that the line |a| is at a right angle to the line |b| 40 Points Y ais Think.. What do you know about perpendicular slopes? Fána a = 1/2 6 4 a 2 X ais 2 4 6 -6 -4 -2 b -2 See Answer -4 Fána b = -2 Back to quiz -6

Q4. Look at the picture below, how can you know for a fact that the line |a| is at a right angle to the line |b| 40 Points Y Axis Slope of line a = 1/2 6 If the line |a| is at a right angle to the line |b|, then they should be perpendicular. So, we can say m a x m b = -1 (½) x (-2) = -1 -1 = -1 Yes, we can say for a fact the lines are at right angles to each other. 4 a 2 X Axis 2 4 6 -6 -4 -2 b -2 -4 Slope of line b = -2 Back to quiz -6

Q5. The equation of a line is y = 2x + 4 Where will this line intersect the Y axis? 50 Points See Answer Back to quiz

Q5. Where will this line intersect the Y axis? 50 Points Y Axis The line cuts the y axis at (0,4) 6 There a lots of ways to solve this question. You could draw the line You could use the equation of the line and allow x = 0 and solve y= 2x + 4 y = 2(0) + 4 y = 4 So when x = 0, y =4 4 2 X Axis 2 4 6 -6 -4 -2 -2 -4 Back to quiz -6

Q1. Identify the hypotenuse in the triangle below. 10 Points x z y See Answer Back to quiz

Q1. Identify the hypotenuse in the triangle below. 10 Points x z Hypotenuse y In a right angle triangle the hypotenuse is always opposite the right angle. So the line y is the hypotenuse. Back to quiz

Q2. Postman Pat must travel 14 km to deliver the mail Q2. Postman Pat must travel 14 km to deliver the mail. Can you calculate a shorter distance? 20 Points ? km 6km See Answer 90o Back to quiz 8km

Q2. Postman Pat must travel 14 km to deliver the mail Q2. Postman Pat must travel 14 km to deliver the mail. Can you calculate a shorter distance? 20 Points Using the theorem of Pythagoras We can figure out that the shortest distance to the house is 10km (6)2 + (8)2 = (?)2 36 + 64 = (?)2 100 = (?)2  100 = ? 10km = ? = Shortest Distance 10km 6km 90o 8km Back to quiz

147.3715o Q3. Change the following decimal angle to Degrees, minutes and seconds 30 Points 147.3715o See Answer Back to quiz

Q3. Change the following decimal angle to Degrees, minutes and seconds 30 Points 147.3715 degrees 0.3715 x 60 = 22.29 Ans = 147o 22’ 17.4’’ Back to quiz

89o 41’ 18’’ Q4. Change the following DMS angle to Degrees and decimals 40 Points 89o 41’ 18’’ See Answer Back to quiz

Q4. Change the following DoM’S’’ angle to Degrees and decimals 40 Points 89o 41’ 18’’ 89o = 89o 41 x 1/60 =.683 18 x (1/60) x (1/60) = .005 Back to quiz Answer: 89.688o

Q5. Find the angle x, that the ramp makes with the ground 50 Points 3 metres 90o x See Answer 4 metres Back to quiz

Q5. Find the angle x, that the ramp makes with the ground 50 Points Using tan x= opposite/adjacent Tan x = ¾ X = Tan-1 ¾ X = 36.86o 3 metres 90o x 4 metres Back to quiz

Q1. Find the missing angle below. Give a reason for your answer 100 Points ? See Answer Back to quiz

Q1. Find the missing angle below. Give a reason for your answer 100 Points 140o Theorem: The angle at the centre of a circle standing on a given arc is twice the angle at any point of the circle standing on the same arc Back to quiz

Q2. Find the missing angle θ below. Give a reason for your answer 100 Points 140o θ See Answer Back to quiz

Q2. Missing angle θ = 26o 100 Points 140o Reason: Back to quiz Each angle in a semi-circle is a right angle

Q3. How high is the biker from the river surface? 100 Points Note: Assume triangle in diagram is a right angle triangle 20 metres x 12 metres 8 metres See Answer Back to quiz

Q3. How high is the biker from the river surface? 100 Points Note: Assume triangle in diagram is a right angle triangle 20 metres x 12 metres 8 metres Back to quiz Using theorem of Pythagoras, biker is 16m + 8m = 24 metres from the river surface

Q4. Can Joe make a triangle from the 3 strips below Q4. Can Joe make a triangle from the 3 strips below? Give a reason for your answer. 100 Points 20 cm 8 cm See Answer Back to quiz 5 cm

Q4. Can Joe make a triangle from the 3 strips below Q4. Can Joe make a triangle from the 3 strips below? Give a reason for your answer. 100 Points 8 cm 5 cm 20 cm No matter how hard he tries, Joe will not be able to make a triangle from these 3 strips. This is because of the theorem that states: 2 sides of a triangle must be longer than the third. In this case 5 + 8 < 20 Back to quiz

Q5. Paul the Penguin is trying to catch some dinner Q5. Paul the Penguin is trying to catch some dinner. How long is his fishing line? 100 Points 1 m Fishing Line ? See Answer 90o 80cm Back to quiz

100 Points Q5. Paul the Penguin is trying to catch some dinner. How long is his fishing line? There are many ways to figure this out, here’s one example using Pythagoras: Remember 1m = 100cm 1 m Fishing Line ? 90o 80cm Back to quiz

Interactive Geometry Quiz Rules 1. Students get into teams of 3 or 4 people 2. Each Team must pick a category and a value e.g. “Tricky Triangles” then pick a point value, e.g. “30 points” 3. Teams can start with any topic and any value on the board. 4. When a Team chooses a category and a point value, then the question is revealed. The Team then has two options; i. PASS – Question goes back into play, no points lost and any other Team can choose this question. ii. PLAY – Team answers the question 5. If the answer is CORRECT, the Team is awarded the number of points for this question, HOWEVER, if the answer is INCORRECT, then the Team’s score will be DEDUCTED by this amount. 6. The winning TEAM is decided by who has the most points at the end of the game. 7. Teachers decision is final BACK TO GAME