Download Post-Learning Assessment Year 9 Module 3

Post-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:
Post-Learning Assessment Mark:
50
Teacher Comment:
Unit 8
1. ABC is a triangle.
AB = 9 cm
AC = 7 cm
BC = 6 cm
Use ruler and a pair of compasses to construct an accurate drawing of triangle ABC.
The line BC has been drawn for you.
C
B
(2)
2. Use ruler and a pair of compasses to construct the perpendicular bisector of
the line AB.
A
B
(2)
3. Triangle ABC is shown below.
a) Mark with a cross (x) angle ACB on the diagram above.
(1)
b) State whether angle ACB is acute or obtuse. ……………………………………………
(1)
c) Use a ruler and pair of compasses to construct the angle bisector of angle ACB.
(2)
Unit 9
4. Here are two triangles.
Diagrams are NOT accurately drawn
The larger triangle is an enlargement of the small triangle with a scale factor of 3.
Find the value of:
a)
𝑤 ……………………………………………..
(1)
b)
𝑥 ……………………………………………..
(1)
c)
𝑦 …………………………………………….
(1)
5. Enlarge trapezium A by a scale factor of 3:
(2)
1
6. Enlarge triangle B by a scale factor of :
2
(2)
7. Two triangles are shown in the diagram below.
45°
45°
Not drawn to scale
a) Give a reason why angles ECD and ACB are equal.
…………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………(1)
b) What can you say about angles DBA and BDE? Give a reason for your answer.
…………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………(2)
c) Are triangles ABC and CDE congruent? How do you know?
…………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………(2)
8. PQRS is a quadrilateral.
P
S
Q
R
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 QSR.
…………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………… (2)
9. Enlarge triangle A by scale factor 2 using (4,1 ) as the centre of enlargement.
(3)
y
5
4
3
2
1
–5
–4
–3
–2
–1
O
–1
–2
–3
–4
–5
1
2
3
x
4
5
6
7
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 ABC.
………………………………………………………………………………………………………………………… (1)
12.Which of the statements below describe the properties of a rectangle? (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 pentagon add up to 540°. 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 shape:
Not drawn to scale
a) Angle a …………………………………………………………………
b) Angle b …………………………………………………………………
(1)
(1)
16. Find the size of the missing angle in this shape:
…………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………… (2)
17.
This is part of the design of a pattern found on a floor mosaic.
It is made up of a 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 36°.
Work out the number of sides of the polygon.
……………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………… (2)
19.
The size of each exterior angle of a polygon is 50°.
Will this polygon tessellate? You must explain your answer clearly.
……………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………… (2)
Finishing task
You are given these three tiles:
Put all three pieces together so that they meet edge-to-edge to make a shape which
has reflection symmetry.
How many different shapes can you make?
Can you make a shape that has rotation symmetry?
How many different shapes can you make?
Can you make one with:
- Reflection symmetry AND rotational symmetry?
- Reflection symmetry ONLY
- Rotational symmetry ONLY?