Year 7 Geometry: free practice test with answers

Sample geometry questions with answers

Try each one before you open the answer.

1. Points, lines, intervals and angles

   Classify each angle as acute, right, obtuse, straight, reflex or a revolution:

   (a) $37°$ (b) $90°$ (c) $145°$ (d) $180°$ (e) $212°$ (f) $360°$

   Show the answer

   Key idea: Acute is between $0°$ and $90°$, obtuse between $90°$ and $180°$, reflex between $180°$ and $360°$.

   1. (a) $0° < 37° < 90°$: acute
   2. (b) exactly $90°$: right
   3. (c) $90° < 145° < 180°$: obtuse
   4. (d) exactly $180°$: straight
   5. (e) $180° < 212° < 360°$: reflex
   6. (f) exactly $360°$: revolution

   Answer: (a) acute (b) right (c) obtuse (d) straight (e) reflex (f) revolution

2. Adjacent and vertically opposite angles

   Angle $a$ and angle $b$ are supplementary. Angle $a = 113°$. Find angle $b$.

   Show the answer

   Key idea: Supplementary angles add to $180°$.

   1. Write the relationship: $a + b = 180°$
   2. Substitute the known angle: $113° + b = 180°$
   3. Solve for $b$: $b = 180° - 113° = 67°$

   Answer: $b = 67°$

3. Solving compound problems with parallel lines

   Two horizontal lines $AB$ and $CD$ are parallel, with $AB$ above $CD$, and $A$ and $C$ on the left. A transversal $EF$ crosses $AB$ at $G$ and $CD$ at $H$, with $E$ above line $AB$ and $F$ below line $CD$. $\angle AGH = 72°$. Find $\angle DHF$, giving reasons.

   Show the answer

   Key idea: Co-interior angles on parallel lines add to $180°$, and vertically opposite angles are equal.

   1. $\angle AGH$ and $\angle GHC$ are co-interior (both between the parallel lines, on the left of the transversal), so $\angle GHC = 180° - 72° = 108°$
   2. $\angle DHF$ is vertically opposite $\angle GHC$, so $\angle DHF = 108°$

   Answer: $\angle DHF = 108°$

4. Classifying and constructing triangles

   A triangle has sides of length 5 cm, 5 cm and 6 cm. Classify this triangle by its sides and by its angles.

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   Key idea: Classify by sides first (count equal sides), then by angles (check whether any angle is 90° or greater).

   1. By sides: Two sides are equal (both 5 cm), so the triangle is isosceles.
   2. By angles: Use the cosine rule to find the largest angle, which is opposite the longest side (6 cm):\

   $$\cos C = \frac{5^2 + 5^2 - 6^2}{2 \times 5 \times 5} = \frac{25 + 25 - 36}{50} = \frac{14}{50} = 0.28$$

   3. Since $\cos C = 0.28 > 0$, angle $C$ is acute. The other two angles are equal and also acute (they must each be less than 90° because the triangle's angles sum to 180° and $C$ is already acute with the two remaining angles sharing what is left).
   4. All three angles are acute, so the triangle is acute.

   Answer: Isosceles and acute-angled triangle.

5. Angle sum of a triangle

   A triangle has interior angles of $47°$ and $86°$. Find the third interior angle.

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   Key idea: The interior angles of any triangle add to $180°$.

   1. Write the angle sum equation: $47 + 86 + x = 180$
   2. Add the known angles: $133 + x = 180$
   3. Subtract $133$ from both sides: $x = 180 - 133 = 47$

   Answer: The third angle is $47°$.

6. Symmetry

   State the number of lines of symmetry and the order of rotational symmetry of:

   (a) a square (b) a rectangle that is not a square (c) an equilateral triangle (d) a parallelogram that is not a rectangle or a rhombus

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   Key idea: A line of symmetry folds a shape onto itself. The order of rotational symmetry is the number of times a shape matches itself in one full turn.

   1. (a) Square: $2$ diagonals and $2$ lines through midpoints of opposite sides, so $4$ lines; it matches itself every quarter turn, order $4$
   2. (b) Rectangle: $2$ lines through midpoints of opposite sides (the diagonals do not work); it matches itself every half turn, order $2$
   3. (c) Equilateral triangle: $3$ lines, one from each vertex to the midpoint of the opposite side; order $3$
   4. (d) Parallelogram: no fold works, so $0$ lines; it matches itself after a half turn about its centre, order $2$

   Answer: (a) $4$ lines, order $4$ (b) $2$ lines, order $2$ (c) $3$ lines, order $3$ (d) $0$ lines, order $2$

7. Translation

   Point $A$ has coordinates $(3, -2)$.

   (a) Translate $A$ by 4 units left and 3 units up. Write the new coordinates.

   (b) Reflect your answer from (a) across the $y$-axis. Write the final coordinates.

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   Key idea: A translation left subtracts from the $x$-coordinate; a translation up adds to the $y$-coordinate. Reflecting across the $y$-axis changes the sign of the $x$-coordinate only.

   1. Start with $A = (3, -2)$.
   2. Translate 4 left and 3 up: $x$-coordinate $= 3 - 4 = -1$, $y$-coordinate $= -2 + 3 = 1$. So the translated point is $(-1, 1)$.
   3. Reflect $(-1, 1)$ across the $y$-axis: change the sign of the $x$-coordinate. $x$-coordinate $= -(-1) = 1$, $y$-coordinate stays $1$.
   4. Final coordinates: $(1, 1)$.

   Answer: (a) $(-1, 1)$ (b) $(1, 1)$

8. Drawing solids

   A triangular prism has two triangular ends joined by rectangular faces.

   (a) How many faces does it have?

   (b) How many edges does it have?

   (c) How many vertices does it have?

   Show the answer

   Key idea: Count the faces, edges and vertices of each end and the parts joining them.

   1. Faces: $2$ triangles and $3$ rectangles, so $5$.
   2. Edges: $3$ on each triangle plus $3$ joining them, so $9$.
   3. Vertices: $3$ on each triangle, so $6$. (Check: $5 + 6 - 9 = 2$.)

   Answer: (a) $5$ (b) $9$ (c) $6$

Free worksheets for this chapter

Worked examples and a free PDF with answers for each topic.

• Year 7 angles worksheet
• Year 7 geometry worksheet
• Year 7 angles in triangles and quadrilaterals worksheet
• Year 7 transformations on the cartesian plane worksheet
• Year 7 volume worksheet