Download Unit 8 - Mathematics Mastery

Pre-Learning
Assessment
Year 9 Module 3: 2D Geometry
Name: ………………………………………………………………….
Class: ……………………………………………………………………
Teacher: ……………………………………………………………….
You need:
 A Pen
 A Pencil
 A Ruler
 A protractor
 A pair of
compasses
What are we learning this half term?
Unit 8: Constructions

In this unit you will learn some new constructions involving bisecting angles and lines as well as a reminder of
constructions involving triangles and quadrilaterals
Unit 9: Congruence and similarity

In this unit you will learn about congruent triangles and the conditions for congruency. You will also explore
similar shapes using your knowledge of fractions and scale factors to help you.
Unit 10: Triangles and quadrilaterals

In this unit you will deepen your understanding of triangle and quadrilateral properties, looking at symmetry
properties and also the diagonal properties of quadrilaterals.
Unit 11: Angles in polygons

In this unit, you will extend your knowledge of angles in triangles and quadrilaterals to other polygons by
exploring interior and exterior angles and the relationships between them.
Pre-Learning Assessment Mark:
50
Teacher Comment:
Unit 8
1. ABC is a triangle.
A
8 cm
B
6 cm
10 cm
C
AB = 8 cm
AC = 6 cm
BC = 10 cm
Use ruler and a pair of compasses to construct an accurate drawing of triangle ABC.
The line BC has been drawn for you.
B
C
(2)
2. Use ruler and a pair of compasses to construct the perpendicular bisector of
the line PQ.
P
Q
(2)
3. Triangle ABC is shown below.
a) Mark with a cross (x) angle ABC on the diagram above.
(1)
b) State whether angle ABC is acute or obtuse. ……………………………………………
(1)
c) Use a ruler and pair of compasses to construct the angle bisector of angle ABC.
(2)
Unit 9
4. Here are two trapezia.
xº
45º
24 cm
6 cm
y cm
16 cm
2 cm
w cm
Diagrams are NOT accurately drawn
The larger trapezium is an enlargement of the small trapezium with a scale factor of
4.
Find the value of:
a)
𝑤 ……………………………………………..
(1)
b)
𝑥 ……………………………………………..
(1)
c)
𝑦 …………………………………………….
(1)
5. Enlarge triangle A by a scale factor of 3:
(2)
1
6. Enlarge trapezium B by a scale factor of :
2
B
(2)
7. Two triangles are shown in the diagram below.
A
40
E
B
C
Not drawn to scale
40
D
a) Give a reason why angles ECD and ACB are equal.
…………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………(1)
b) What can you say about angles BAC and DEC? Give a reason for your answer.
…………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………(2)
c) Are triangles ABC and CDE congruent? How do you know?
…………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………(2)
8. PQRS is a quadrilateral.
a) What is the mathematical name for the shape above?
…………………………………………………………..
(1)
b) What can you say about the lengths of sides PQ and SR?
…………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………… (1)
c) Show that triangle PQS is congruent to triangle RSQ.
…………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………… (2)
9. Enlarge triangle A by scale factor 2 using (1, 1) as the centre of enlargement.
y
5
4
3
2
A
1
–5
–4
–3
–2
–1 O
1
2
3
x
4
5
6
7
–1
–2
–3
–4
–5
(3)
Unit 10
10.
What is the mathematical name given to the triangle above?
…………………………………………………………………………………………………………………………… (1)
11.
a) What is the mathematical name of the shape above?
............................................................................................................................... (1)
b) Measure and write down the size of angle RQP
………………………………………………………………………………………………………………………… (1)
12.Which of the statements below describe the properties of a rhombus? (You
may select more than one answer).
a. The diagonals are perpendicular
b. The diagonals are equal in length
c. The diagonals bisect each other
d. All sides are equal in length
e. All angles are the same size
(3)
13. For each quadrilateral below, draw in all of the lines of symmetry (if any).
(4)
Unit 11
14. The interior angles of a quadrilateral add up to 360°. Can you explain why
this is? You may use the diagram below to help.
…………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………… (2)
15. Find the size of the missing angle in this kite:
110
a
Not drawn to scale
84
b
a) Angle a …………………………………………………………………
(1)
b) Angle b …………………………………………………………………
(1)
16. Find the size of the missing angle in this shape:
88
141
63
𝑥
NOT DRAWN TO SCALE
91
…………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………… (2)
17.
Diagram NOT
accurately drawn
x°
y°
This is part of the design of a pattern found on a floor mosaic.
It is made up of a regular hexagon, squares and equilateral triangles.
Write down the sizes of the angles marked 𝑥° and 𝑦°.
𝑥 = …………………………………………………
(1)
𝑦 = ………………………………………………..
(2)
18. The size of each exterior angle of a polygon is 40°.
Work out the number of sides of the polygon.
……………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………… (2)
19.
The size of each exterior angle of a polygon is 30°.
Will this polygon tessellate? You must explain your answer clearly.
……………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………… (2)
Finishing task
How many diagonals does each of the shapes above have?
Can you predict how many diagonals a hexagon will have? And a heptagon? Explain
how you made your predictions.
Sketch a hexagon and heptagon to test your hypothesis.
Can you predict how many diagonals a decagon would have?
What about a 15 sided shape?