Download 1 - SMC-Math

NH 1001
N.C.E.A. LEVEL 1.9
GEOMETRIC REASONING.
GEOMETRY QUILT.
5.
2 CREDITS.
25 Minutes
You should show ALL working.
1.
Francis is making a quilt using hexagonal shapes as shown below.
The hexagon has two lines of symmetry as marked with dashed lines.
F
E
140o
G
110o
A
D
B
C
Find the angle GBA.
2.
Another quilt is made from triangles. Part of the design is shown below.
D
A
C
22o
110o
E
B
Find the angle ABD.
3.
C
42o
The border of a quilt has triangles like the one shown below.
C
BE and CD are parallel.
B
84o
32o
A
Find the angle EDC.
E
D
4.
Xavier initials the quilt in the bottom corner.
AF and NI are parallel.
B
E
64o
A
C
D
F
G
57o
N
K
L
H
I
J
Find the angle BGK.
You MUST give geometric reasons for your answer.
5.
Another person makes pillow quilts using only regular hexagons, similar to the one shown below.
a)
Explain clearly what it meant by a polygon being classified as ‘regular’.
b)
Why is it possible that some regular polygon shapes can be used for quilting but other polygons
cannot.
6.
Nicki uses patches of triangles and trapeziums to make the letter N.
C
F
E
D
B
G
52o
A
H
I
BG and AH are parallel.
AC and IF are parallel.
Triangle BCD is isosceles.
Find the angle CIF.
You MUST give geometric reasons for your answer.
7.
In the figure below, ABCDE is a regular pentagon.
A
x
E
B
D
Calculate the size of angle DAC (marked x).
You MUST give clear geometric reasons for your answer.
C
NH 1001
Assessment Schedule for Achievement Standard 1.9
Achievement
Criteria
Use geometric
reasoning to
solve problems.
Achievement with merit
Use, and state,
geometric
reasons in
solving
problems.
No.
One
Code
A
Two
90153:Geometry Quilt
Evidence
GBA = 70o
Judgement
No alternative
A
ABD = 48o
No alternative
Three
A
EDC = 64o
No Alternative
Four
A/M
CDG = 57o
GCD = 64o
BGK = 121o
Five (a)
M
Each interior angle
congruent AND Each
side congruent
Five (b)
M
The sum of the interior
angles at a point must
sum to 360˚.
A/M
Triangle ACI isosceles
AID = 52o
FIH = 52o
CIF = 76o
alt angles, parallel lines
Throughout
vertically oppositeAchievement
angles
Plusof int opp
Merit:
ext angle equals sum
3 of Code M
- allow other
valid chains of
or
reasoning.
- reasons may
4 of code M
be combined
into one
statement.
- A is for
correct angle
without
similar chain
with ACD
of
base
reasoning
angle isosceles triangle
corresp angles, parallel lines
angles on a line
Six
Seven
M
AED = 108˚
int angle of reg pentagon
EAD = 36˚
base angle isosceles
triangle
ABC = 108˚
int angle of reg pentagon
BAC = 36˚
base angle isosceles
triangle
x = 108–(EAD +BAC)
= 36˚
Sufficiency
3 of Code A