Geometry questions test angles, shapes and solids, and your child reasons from angle totals and definitions, not from the diagram's look. Your child is tested at their current year level, and each school selects its own test date.
Angles, shapes and solids, and what must follow from a few facts about them. Edutest calls this area space: year-level maths: numbers, measurement, algebra, space and data.
Our questions are written for children in Years 6–7 applying for Year 7 or 8. At that level, your child needs angles on a straight line, around a point and in a triangle, and the types of triangles and four-sided shapes. They also need the faces, edges and vertices of prisms and pyramids, plus symmetry, reflections, rotations and translations.
Around Year 7 come the angles made where a line crosses parallel lines. In our questions, naming a shape is never enough: your child is given a few facts and asked what they prove.
The six totals below, because an angle question comes down to one of them and some subtraction. Learn them with the reason beside each, so a forgotten total can be rebuilt in the test.
Two shape facts matter just as much. An isosceles triangle has two equal sides and two equal angles. Where two straight lines cross, the opposite angles are equal.
Angle totals worth knowing
Where
Angles add to
Why
On a straight line
180°
Half a full turn
Around a point
360°
A full turn
In a triangle
180°
Its corners torn off make a straight line
In a four-sided shape
360°
A diagonal splits it into two triangles
In a pentagon
540°
Lines from a corner split it into three triangles
In any polygon
(sides − 2) × 180°
There are two fewer triangles than sides
How should your child work a geometry question?
Write down every known fact before choosing a total. Geometry answers come from what is given, so a written list keeps your child from trusting a diagram that may not be drawn to scale.
Write down what you know
Note every given angle and side, and every pair that must be equal because of the shape.
Start from a total
Choose the angle total that fits the shape, then subtract the angles you know.
Check every case
If a given angle could sit in different positions, try each and keep the one that fits all the facts.
Test always with an awkward example
For a statement about every rhombus or every rectangle, picture a stretched or leaning one. A counterexample rules a statement out.
Four worked examples
These are in the style of Edutest Mathematics, and the last one is the hardest. Each one shows the answer and the working. Read them with your child and name the fact or total each one starts from.
Ask which option looked right at first, and which fact led there. A wrong total is a gap to learn; a right total with a wrong option may mean a case was missed.
Worked explanation 1
A solid has 5 faces, 9 edges and 6 vertices (corners). Which solid is it?
AA.
Triangular prism
BB.
Square-based pyramid
CC.
Triangular-based pyramid
DD.
Pentagonal-based pyramid
Answer: A
Answer: A (Triangular prism)
A triangular prism has two triangle ends and three rectangle sides, so 2 + 3 = 5 faces. Each triangle has 3 edges, and 3 more edges join the triangles, so 3 + 3 + 3 = 9 edges. Each triangle has 3 corners, so there are 6 vertices. All three numbers match.
The trap: Square-based pyramid tempts children because it also has 5 faces, but it has only 8 edges and 5 vertices.
Why the other options are wrong
B (Square-based pyramid): Has 5 faces, but only 8 edges and 5 vertices.
C (Triangular-based pyramid): Has 4 faces, 6 edges and 4 vertices.
D (Pentagonal-based pyramid): Has 6 faces, 10 edges and 6 vertices.
Worked explanation 2
A triangle has two equal sides. One of its angles is 70°, and its other two angles are different sizes from each other. What is the size of its smallest angle?
AA.
40°
BB.
55°
CC.
70°
DD.
110°
Answer: A
Answer: A (40°)
Two equal sides means two equal angles, and the three angles add to 180°. If 70° were the odd angle out, the other two would share 110° equally, making 55° and 55°; but they must be different, so that cannot be it. So 70° is one of the equal pair, and the angles are 70°, 70° and 180° − 140° = 40°. The smallest angle is 40°.
The trap: 55° tempts children who assume 70° is the angle between the two equal sides and halve 110°, without checking that the other two angles must be different sizes.
Why the other options are wrong
B (55°): Treats 70° as the odd angle, giving 55° and 55°, which are equal, not different.
C (70°): 70° is the largest angle here (it appears twice), not the smallest.
D (110°): 110° is 180° − 70°, the total of the other two angles, not one angle.
Worked explanation 3
A rhombus has four equal sides. Which statement is true for every rhombus?
AA.
Its diagonals are always equal in length.
BB.
Its diagonals always cross at right angles.
CC.
All four of its angles are always right angles.
DD.
It always has exactly one line of symmetry.
Answer: B
Answer: B (Its diagonals always cross at right angles.)
Picture a rhombus that is not a square, like a diamond that leans over. Its diagonals have different lengths and its angles are not right angles, so A and C are not always true. It has two lines of symmetry, one along each diagonal, so D is false. In every rhombus the diagonals cross at right angles and cut each other in half. The answer is B.
The trap: A tempts children who picture a square, which is a special rhombus with equal diagonals. In a leaning rhombus one diagonal is longer than the other.
Why the other options are wrong
A (Its diagonals are always equal in length.): Only true when the rhombus is a square.
C (All four of its angles are always right angles.): Only true when the rhombus is a square.
D (It always has exactly one line of symmetry.): A rhombus has two lines of symmetry, along its diagonals (a square has four).
Worked explanation 4
In the diagram, a large triangle has two lines drawn from its top corner down to its base, and one line across that is parallel to the base and runs from one sloping side to the other. How many triangles of any size are there in the diagram?
AA.
3
BB.
6
CC.
9
DD.
12
Answer: D
Answer: D (12)
Every triangle in this diagram has its top at the top corner, with two of the four lines from that corner as its sides (the two sloping sides and the two drawn lines). Choosing two of four lines can be done in 3 + 2 + 1 = 6 ways. Each pair makes one triangle closed off by the line across and one closed off by the base, so there are 6 × 2 = 12 triangles. The pieces below the line across are four-sided, so they add no extra triangles.
The trap: 6 tempts children who count only the triangles standing on the base and miss the smaller triangles above the line across.
Why the other options are wrong
A (3): Counts only the three smallest triangles at the top.
B (6): Counts only the triangles that sit on the base.
C (9): Counts the 6 on the base and the 3 small ones at the top, but misses the 3 larger triangles above the line across.
How does your child count shapes in a figure?
With a system, not a long stare. Counting by eye misses the larger shapes built from several pieces.
Count by a fixed part. A triangle with a line from its top corner to its base holds three triangles: the two parts and the whole. With more lines from that corner, each pair of lines makes a triangle, so your child counts the pairs.
For solids, one check works on every prism and pyramid: faces plus vertices, minus edges, always equals 2. If the counts in an option break that rule, the option is wrong.
What traps should your child watch for?
Each trap below is a picture in the head that the facts don't support. When your child falls for one, name it together, then sketch the awkward case before answering the next question.
Picturing the neat case. A square is a special rhombus, so a statement true of squares can fail for a leaning rhombus. Picture the general shape.
Assuming which angle is which. In an isosceles triangle, the given angle may be one of the equal pair or the odd one out. Check both.
Using the wrong total. A pentagon's angles add to 540°, not 360°.
Matching on one count. A square-based pyramid has as many faces as a triangular prism, but different numbers of edges and vertices. Check all three.
What does no ruler mean for geometry?
Every length and angle has to be worked out, not measured. On test day Edutest doesn't allow calculators, rulers, dictionaries, working-out paper, mobile phones, smart watches and fitness trackers.
An angle that looks like a right angle counts as one when the question says so or marks it, not because it looks square. Reasoning from what is stated is the habit these questions test, so practise at home without a ruler too.
Handle real solids. Count the faces, edges and vertices of a cereal box, a tent or a triangular chocolate box, then check the count with the faces-plus-vertices rule.
Draw shapes that break the obvious picture: a rhombus that isn't a square, a rectangle that isn't a square, a triangle with an obtuse angle. Area and perimeter sit on the measurement page.
In the app, the geometry lesson has an Interactive version and Notes. There are also drills by section and topic; a free account drills the free test's questions, and a paid plan opens the rest.
Four questions show the method; the Mathematics section of Practice test 1 shows whether your child can use it against the clock. Afterwards, results by skill show whether geometry is the area costing marks.
