Geometry Quiz
Read the Rules of
the Game
Tricky
Triangles
Theorems
Symmetry
Coordinate
Geometry
Trigonometry
Super
Bonus
Round
10 Points
10 Points
10 Points
10 Points
10 Points
100 A
20 Points
20 Points
20 Points
20 Points
20 Points
100 B
30 Points
30 Points
30 Points
30 Points
30 Points
100 C
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
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How many degrees
in a Straight Angle?
10
Points
180
There are 180 degrees in a
Straight Angle (Axiom 3)
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Q1. Find the value of
the missing angle in the
shape below
?
10
Points
See Answer
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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
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Q2. The triangle below is
isosceles.. Why?
20
Points
See Answer
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Q2. The triangle below is isosceles.
Why?
20
Points
Theorem : In an isosceles triangle
the angles opposite the equal sides
are equal.
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Q3. What is the missing
30
angle?
Points
?
See Answer
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Q3. What is the missing angle?
30
Points
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 the
interior opposite angles.
100o + 50o = 150o
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Q4. Find the missing length?
40
Points
?
See Answer
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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
25 = ? So , 5 = the missing length
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Q5. Are the triangles below,
congruent, similar, totally
50
different? Give a reason for your Points
answer
See Answer
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Q5. These triangles are “Similar”
50
Points
Theorem: If two triangles are similar,
then their sides are proportional,
in order.
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Q1. Find the missing angle. Give a
reason for your answer.
10
Points
See Answer
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Q1. Find the missing Angle. Give a
reason for your answer
10
Points
95o
Theorem: Vertically opposite angles
are equal in measure.
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Q2. Find the missing length in the
parallelogram below. Give a reason
for your answer.
?
20
Points
See Answer
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Q2. Find the missing length in the parallelogram
below. Give a reason for your answer.
3
Theorem: The diagonals of a
parallelogram bisect each other.
20
Points
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Q3. Are the lines |a| and |b| below
parallel? Give a reason for your answer
30
Points
See Answer
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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).
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Two lines are parallel if and only if
for any transversal, corresponding angles are equal.
Q4. Give 2 reasons why you can be sure the
shape below is a parallelogram
40
Points
See Answer
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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
Theorem: In a parallelogram, opposite
sides are equal and opposite angles are
equal.
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Q5. Find the values of x and y below. What
theorem supports you answer?
50
Points
X
See Answer
Y
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Q5. Find the values of x and y below. What
50
theorem supports you answer?
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.
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Q1. Copy the shape and draw in the
axis of symmetry
10
Points
See Answer
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Q1. Copy the shape and draw in the
axis of symmetry
10
Points
1 Axis of
symmetry
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Q2. How many axes of symmetry
does this shape have?
20
Points
See Answer
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Q2. How many axes of symmetry
does this shape have?
20
Points
2 Axis of
symmetry
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Q3. Copy this shape and draw its
reflection through the given line 30
T
Points
Line of Reflection
See Answer
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Q3. Copy this shape and draw its
reflection through the given line 30
T
Points
Line of Reflection
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T
Q4. Copy this shape and draw its
reflection through the given line 40
E
Line of Reflection
Points
See Answer
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Q4. Copy this shape and draw its
reflection through the given line 50
E
Points
Line of Reflection
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Q5. Copy this shape and draw its
reflection through the Point D
50
Points
A
B
C
See Answer
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Q5. Copy this shape and draw its
reflection through the Point D
50
Points
A
B
C
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Q1. Name the points A and B
Y Axis
3
A
10
Points
2
1
X Axis
0
-3
-2
-1
0
1
2
3
-1
-2
-3
B
See Answer
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Q1. Name the points A and B
3
A
10
Points
2
(-3, 2)
1
0
-3
-2
-1
0
1
2
3
-1
-2
-3
B
(2, -2)
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Q2. Find the distance between Scooby
20
and his snacks.
Points
Y Axis
15
10
(-10, 10)
5
X Axis
0
-15
-10
-5
0
5
10
15
-5
See Answer
-10
-15
(15,-10)
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Q2. Find the distance between Scooby
20
and his snacks.
Yummy!
2
15
(10  (15)) 2  (10  (10) 2
10
(-10, 10)
-15
-10
(10  15) 2  (10  10) 2
5
-5
Points
2
( x2  x1 )  ( y2  y1 )
Y Axis
X Axis
(25) 2  (20)
15
-5
625  400
-10
1025
0
0
-15
5
10
(15,-10)
32 _ units
Scooby must walk
32units to get his
yummy snacks!
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Q3. A jeweller needs to cut this gold chain
exactly in half, at what point should he make the cut?
Y Axis
(4,6)
6
Mmm..
Where
should I cut
this chain?
4
2
-6
-4
-2
0
0
30
Points
X Axis
2
4
6
-2
-4
(-6,-6)
-6
See Answer
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Q3. A jeweller needs to cut this gold chain
exactly in half, at what point should he make the cut?
Y Axis
(4,6)
6
4
2
(-1,0)
-6
-4
-2
0
0
-2
-4
(-6,-6)
-6
X Axis
2
4
6
Find the
Mid Point
30
Points
x1  x2 y1  y2
,
2
2
4  (6) 6  (6)
,
2
2
2 0
,
2 2
1, 0
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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
Slope of
line |a| = 1/2
Think.. What
do you know
about
perpendicular
slopes?
6
4
a
40
Points
2
-6
-4
-2
b
0
0
X Axis
2
4
6
-2
See Answer
-4
-6
Slope of
line |b| = -2
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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
4
a
2
-6
-4
-2
b
0
0
X Axis
2
4
6
-2
Yes, we can say for a fact the lines
are at right angles to each other.
-4
-6
m a x m b = -1
(½) x (-2) = -1
-1 = -1
Slope of
line b = -2
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Q5. The equation of a line is
y = 2x + 4
50
Points
Where will this line intersect the Y axis?
See Answer
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Q5. Where will this line intersect the Y
axis?
50
The line cuts
the y axis at
(0,4)
Points
Y Axis
6
4
2
-6
-4
-2
0
0
-2
-4
-6
X Axis
2
4
6
There a lots of ways to solve this
question.
1. You could draw the line
2. 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
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Q1. Identify the hypotenuse in the
triangle below.
10
Points
x
z
y
See Answer
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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.
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Q2. Postman Pat must travel 14 km to
deliver the mail. Can you calculate a
20
shorter distance?
Points
? km
6km
See Answer
90o
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8km
Q2. Postman Pat must travel 14 km to
deliver the mail. Can you calculate a
20
shorter distance?
Points
10km
6km
90o
8km
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
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Q3. Change the following decimal angle to
Degrees, minutes and seconds
30
Points
o
147.3715
See Answer
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Q3. Change the following decimal angle to
Degrees, minutes and seconds
147.3715 degrees
30
Points
0.3715 x 60
= 22.29
Ans =
o
147
22’ 17.4’’
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Q4. Change the following DMS angle to
Degrees and decimals
o
89
41’ 18’’
40
Points
See Answer
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Q4. Change the following DoM’S’’ angle to
Degrees and decimals
o
89
o
89
41’ 18’’
40
Points
o
89
=
41 x 1/60 =.683
18 x (1/60) x (1/60) = .005
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Answer:
o
89.688
Q5. Find the angle x, that the ramp makes
with the ground
50
Points
3 metres
90o
x
4 metres
See Answer
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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
3 metres
X = 36.86o
90o
x
4 metres
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Q1. Find the missing angle below.
Give a reason for your answer
100
Points
?
See Answer
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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
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Q2. Find the missing angle θ below.
Give a reason for your answer
100
Points
140o
θ
See Answer
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Q2. Missing angle θ = 26o
100
Points
26o
.
140o
90o
Reason:
Each angle in a semi-circle is a right angle
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Q3. How high is the biker from the
river surface?
100
Points
x
12 metres
Note: Assume
triangle in
diagram is a
right angle
triangle
8 metres
See Answer
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Q3. How high is the biker from the
river surface?
100
Points
Note: Assume
triangle in
diagram is a
right angle
triangle
x
12 metres
8 metres
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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 100
for your answer.
Points
20 cm
8 cm
See Answer
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5 cm
Q4. Can Joe make a triangle from
the 3 strips below? Give a reason 100
for your answer.
Points
8 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
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Q5. Paul the Penguin is trying to
catch some dinner. How long is his100
fishing line?
Points
Fishing Line
?
90o
80cm
See Answer
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100
Q5. Paul the Penguin is trying to catch some
Points
dinner. How long is his fishing line?
There are many ways to figure this out, here’s one
example using Pythagoras: Remember 1m = 100cm
1002  802  ?2
10000  6400  ?2
10000  6400  ?2
3600  ?2
Fishing Line
?
90o
80cm
3600  ?
60  ?
Fishing _ line  60cm
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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
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