geometry quiz 10 points 20 points 30 points 40 points 50 points 10 points 20 points 30 points 40...
TRANSCRIPT
Geometry Quiz
10 Points
20 Points
30 Points
40 Points
50 Points
10 Points
20 Points
30 Points
40 Points
50 Points
10 Points
20 Points
30 Points
40 Points
50 Points
10 Points
20 Points
30 Points
40 Points
50 Points
10 Points
20 Points
30 Points
40 Points
50 Points
TrickyTriangles
100 A
100 B
100 C
100 D
100 E
Super Bonus Round
Theorems Symmetry Coordinate Geometry
Trigonometry
Read the Rules of the Game
How many degrees in a Straight Angle?
?
See Answer
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10 Point
s
How many degrees in a Straight Angle?
180
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There are 180 degrees in a Straight Angle (Axiom 3)
10 Point
s
Q1. Find the value of the missing angle in the shape below
See Answer
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10 Point
s
?
Q1. Find the value of the missing angle in the shape below
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10 Point
s
44o
Theorem : The angles in any triangle add to 180°50 + 86 + ? = 180136 + ? = 180? = 180 – 136 = 44
Q2. The triangle below is isosceles.. Why?
See Answer
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20 Point
s
Q2. The triangle below is isosceles. Why?
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20 Point
s
Theorem : In an isosceles triangle the angles opposite the equal sides
are equal.
Q3. What is the missing angle?
See Answer
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30 Point
s
?
Q3. What is the missing angle?
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30 Point
s
150o
There are at least 2 ways you can get the answer;
1. Axiom 3: The number of degrees in a straight angle = 180o
30o + ? = 180? = 180o-30o =150o
2. Theorem 6: Each exterior angle of a triangle is equal to the sum of theinterior opposite angles.100o + 50o = 150o
Q4. Find the missing length?
See Answer
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40 Point
s
?
Q4. Find the missing length
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40 Point
s
[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 length25
Q5. Are the triangles below,congruent, similar, totally different? Give a reason for your answer
See Answer
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50 Point
s
Q5. These triangles are “Similar”
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50 Point
s
Theorem: If two triangles are similar, then their sides are proportional,in order.
Q1. Find the missing angle. Give a reason for your answer.
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10 Point
s
See Answer
Q1. Find the missing Angle. Give a reason for your answer
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10 Point
s
Theorem: Vertically opposite angles are equal in measure.
95o
Q2. Find the missing length in the parallelogram below. Give a reason for your answer.
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20 Point
s
See Answer
?
Q2. Find the missing length in the parallelogram
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20 Point
s
3
below. Give a reason for your answer.
Theorem: The diagonals of a parallelogram bisect each other.
Q3. Are the lines |a| and |b| below parallel? Give a reason for your answer
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30 Point
s
See Answer
Q3. Are the lines |a| and |b| below parallel? Give a reason for your answer
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30 Point
s
No the lines are NOT parallelTheorem 5 (Corresponding Angles). Two lines are parallel if and only iffor any transversal, corresponding angles are equal.
Angles are NOT the
same size
Q4. Give 2 reasons why you can be sure the shape below is a parallelogram
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40 Point
s
See Answer
Q4. 2 reasons why we can be sure this shape is a parallelogram.
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40 Point
s
Opposite sides are equal in length
Theorem: In a parallelogram, opposite sides are equal and opposite angles are equal.
Opposite angles are
equal in measure
Q5. Find the values of x and y below. What theorem supports you answer?
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50 Point
s
See Answer
X
Y
Q5. Find the values of x and y below. What theorem supports you answer?
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50 Point
sTheorem: Let ABC be a triangle. If a line l is parallel to BCand cuts [AB] in the ratio s:t, then it also cuts [AC] inthe same ratio.
Q1. Copy the shape and draw in the axis of symmetry
See Answer
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10Point
s
Q1. Copy the shape and draw in the axis of symmetry
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10Point
s
1 Axis of symmetry
Q2. How many axes of symmetry does this shape have?
See Answer
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20Point
s
Q2. How many axes of symmetry does this shape have?
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20Point
s
2 Axis of symmetry
Q3. Copy this shape and draw its reflection through the given line
See Answer
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30Point
sTLine of Reflection
Q3. Copy this shape and draw its reflection through the given line
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30Point
sTT Line of Reflection
Q4. Copy this shape and draw its reflection through the given line
See Answer
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40Point
sELine of Reflection
Q4. Copy this shape and draw its reflection through the given line
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50Point
sE ELine of Reflection
Q5. Copy this shape and draw its reflection through the Point D
See Answer
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50Point
s
A
BC
Q5. Copy this shape and draw its reflection through the Point D
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50Point
s
A
BC
See Answer
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10Point
s
1 2 3
1
2
3
-1-2-3
-1
-2
-3
00
A
B
Q1. Name the points A and BY Axis
X Axis
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10Point
s
1 2 3
1
2
3
-1-2-3
-1
-2
-3
00
A
B
Q1. Name the points A and B
(-3, 2)
(2, -2)
See Answer
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20Point
s
5 10 15
(-10, 10)
10
15
-5-10-15
-5
-10
-15
00
5
(15,-10)
Q2. Find the distance between Scooby and his snacks.
Y Axis
X Axis
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20Point
s
5 10 15
(-10, 10)
10
15
-5-10-15
-5
-10
-15
00
5
(15,-10)
Q2. Find the distance between Scooby and his snacks.
Y Axis
X Axis
2 22 1 2 1
2 2
2 2
2
( ) ( )
( 10 (15)) (10 ( 10)
( 10 15) (10 10)
(25) (20)
625 400
1025
32 _
x x y y
units
Scooby must walk 32units to get his yummy snacks!
Yummy!
See Answer
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30Point
s
2 4 6
4
6
-2-4-6
-2
-4
-6
00
2
Q3. A jeweller needs to cut this gold chain exactly in half, at what point should he make the cut?
Y Axis
X Axis
(4,6)
(-6,-6)
Mmm.. Where
should I cut this chain?
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30Point
s
2 4 6
4
6
-4-6
-2
-4
-6
00
2
Q3. A jeweller needs to cut this gold chain exactly in half, at what point should he make the cut?
Y Axis
X Axis
(4,6)
(-6,-6)
1 2 1 2,2 2
4 ( 6) 6 ( 6),
2 22 0,
2 21,0
x x y y
Find the Mid Point
(-1,0)
-2
See Answer
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40Point
s
2 4 6
4
6
-2-4-6
-2
-4
-6
00
2
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|
Y ais
X ais
a
b
Fána a = 1/2
Fána b = -2
Think.. What do you know
about perpendicular
slopes?
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40Point
s
2 4 6
4
6
-2-4-6
-2
-4
-6
00
2
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|
Y Axis
X Axis
a
b
Slope of line a = 1/2
Slope of line b = -2
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.
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50Point
s
Q5. The equation of a line is
y = 2x + 4
Where will this line intersect the Y axis?
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50Point
s
2 4 6
4
6
-2-4-6
-2
-4
-6
00
2
Q5. Where will this line intersect the Y axis?
Y Axis
X Axis
There a lots of ways to solve this question.1. You could draw the line2. You could use the equation
of the line and allow x = 0 and solve
y= 2x + 4y = 2(0) + 4y = 4So when x = 0, y =4
The line cuts the y axis at (0,4)
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10Point
s
Q1. Identify the hypotenuse in the triangle below.
See Answer
x
y
z
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10Point
s
Q1. Identify the hypotenuse in the triangle below.
x
y
z
In a right angle triangle the hypotenuse is always opposite the right angle. So the line y is the hypotenuse.
Hypotenuse
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20Point
s
Q2. Postman Pat must travel 14 km todeliver the mail. Can you calculate a shorter distance?
See Answer
8km
6km
90o
? km
Using the theorem of PythagorasWe can figure out that theshortest distance to the house is 10km
(6)2 + (8)2 = (?)2
36 + 64 = (?)2
100 = (?)2
100 = ?10km = ? = Shortest Distance
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20Point
s
Q2. Postman Pat must travel 14 km todeliver the mail. Can you calculate a shorter distance?
8km
6km
90o
10km
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30Point
s
Q3. Change the following decimal angle toDegrees, minutes and seconds
See Answer
147.3715o
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30Point
s
Q3. Change the following decimal angle toDegrees, minutes and seconds
147.3715 degrees
0.3715 x 60 = 22.29Ans = 147o 22’ 17.4’’
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40Point
s
Q4. Change the following DMS angle toDegrees and decimals
See Answer
89o 41’ 18’’
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40Point
s
Q4. Change the following DoM’S’’ angle toDegrees and decimals
89o 41’ 18’’89o = 89o 41 x 1/60 =.68318 x (1/60) x (1/60) = .005
Answer: 89.688o
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50Point
s
Q5. Find the angle x, that the ramp makes with the ground
See Answer90o
4 metres
3 metres
x
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50Point
s
Q5. Find the angle x, that the ramp makes with the ground
90o
4 metres
3 metres
x
Using tan x= opposite/adjacent
Tan x = ¾
X = Tan-1 ¾
X = 36.86o
Q1. Find the missing angle below. Give a reason for your answer
See Answer
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100Point
s
?
Q1. Find the missing angle below. Give a reason for your answer
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100Point
s
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
Q2. Find the missing angle θ below. Give a reason for your answer
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100Point
s
140o
θ
See Answer
Q2. Missing angle θ = 26o
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100Point
s
140o
Reason:
26o.
Each angle in a semi-circle is a right angle
90o
Q3. How high is the biker from the river surface?
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100Point
s
See Answer
12 metres
8 metres
20 metre
s
x
Note: Assume triangle in diagram is a right angle triangle
Q3. How high is the biker from the river surface?
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100Point
s
12 metres8 m
etres
20 metre
s
x
Note: Assume triangle in diagram is a right angle triangle
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? Give a reason for your answer.
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100Point
s
See Answer
20 cm
8 cm
5 cm
Q4. Can Joe make a triangle from the 3 strips below? Give a reason for your answer.
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100Point
s
20 cm
8 cm5 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
Q5. Paul the Penguin is trying to catch some dinner. How long is his fishing line?
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100Point
s
See Answer
80cm
1 m
?
90o
Fishing Line
Q5. Paul the Penguin is trying to catch some dinner. How long is his fishing line?
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100Point
s
80cm
1 m
?
90o
Fishing Line
There are many ways to figure this out, here’s one example using Pythagoras: Remember 1m = 100cm
2 2 2
2
2
2
100 80 ?
10000 6400 ?
10000 6400 ?
3600 ?
3600 ?
60 ?
_ 60Fishing line cm
Interactive Geometry Quiz Rules1. 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