Year 9 Shape and Geometry Worksheet - Beginner

Year 9 Shape and Geometry worksheet for Year 9 (Key Stage 3 / Year 7-9 (Ages 11-14)). Beginner level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.

Maths•Key Stage 3 / Year 7-9 (Ages 11-14)•Geometrybeginner

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Year 9 Shape and Geometry: Triangles, Transformations and Scale

Ages 13–14 | Beginner

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Instructions: Work through each activity in order, showing your method in the answer spaces. For calculations, use a calculator where needed and give lengths to 1 decimal place unless an exact value is requested. Assume all diagrams described in words are right-angled where stated.

Pythagoras’ Theorem: Find a Missing Side

For a right-angled triangle, use a² + b² = c², where c is the hypotenuse (the longest side, opposite the right angle). Rearrange the equation when the missing side is a shorter side. Give answers to 1 decimal place where necessary and show your working.

1. A right-angled triangle has shorter sides 6 cm and 8 cm. Find the hypotenuse. [3 marks]

2. A right-angled triangle has hypotenuse 13 cm and one shorter side 5 cm. Find the other shorter side. [3 marks]

3. A right-angled triangle has shorter sides 7 cm and 9 cm. Find the hypotenuse to 1 decimal place. [3 marks]

4. A 10 m ladder rests against a wall. Its foot is 6 m from the wall. How high up the wall does it reach? [3 marks]

Trigonometric Ratios: Choose and Use

Relative to the marked angle, identify the opposite, adjacent and hypotenuse sides. Choose sin = opposite ÷ hypotenuse, cos = adjacent ÷ hypotenuse or tan = opposite ÷ adjacent. Set your calculator to degrees. Give lengths to 1 decimal place and angles to the nearest degree.

1. In a right-angled triangle, an angle is 30° and the hypotenuse is 10 cm. Find the side opposite the angle. [3 marks]

2. In a right-angled triangle, an angle is 60° and the hypotenuse is 12 cm. Find the side adjacent to the angle. [3 marks]

3. In a right-angled triangle, an angle is 45° and the adjacent side is 8 cm. Find the opposite side. [3 marks]

4. In a right-angled triangle, the opposite side is 6 cm and the hypotenuse is 10 cm. Find the angle to the nearest degree. [3 marks]

Describe Transformations

Name the transformation and give all details needed to describe it. For a translation, write the movement as a vector; for a reflection, state the mirror line; for a rotation, state the centre, direction and angle; for an enlargement, state the centre and scale factor.

1. Point A(2, 1) maps to A′(5, 3), and every point moves in the same way. Describe the translation as a vector. [2 marks]

2. Point B(4, 2) maps to B′(−4, 2) under a reflection. State the mirror line. [2 marks]

3. Point C(3, 1) maps to C′(−1, 3) under a 90° anticlockwise rotation about the origin. State the centre and angle of rotation. [2 marks]

4. A shape with vertices (1, 1), (3, 1) and (1, 2) is enlarged from the origin by scale factor 2. Write the coordinates of the image vertices. [3 marks]

Similar Shapes and Scale Factors

Write your answer in the box below.

Similar or Congruent?

Congruent shapes have the same shape and size; similar shapes have the same shape but may have different sizes. Use corresponding side lengths and angles to decide. Give a short reason for each answer.

1. Triangle P has sides 3 cm, 4 cm and 5 cm. Triangle Q has sides 3 cm, 4 cm and 5 cm. Are the triangles congruent, similar but not congruent, or neither? [2 marks]

2. Rectangle R measures 4 cm by 6 cm. Rectangle S measures 8 cm by 12 cm. Are the rectangles congruent, similar but not congruent, or neither? [2 marks]

3. Triangle U has angles 40°, 60° and 80°. Triangle V has angles 40°, 60° and 80°, with different side lengths. Are they congruent, similar but not congruent, or neither? [2 marks]

4. A rectangle measures 3 cm by 5 cm. Another rectangle measures 6 cm by 11 cm. Are the rectangles congruent, similar but not congruent, or neither? Explain using the side ratios. [3 marks]

Answer Key

Activity 1: 10 cm ; 12 cm ; 11.4 cm ; 8 m

Activity 2: 5 cm ; 6 cm ; 8 cm ; 37°

Activity 3: (3, 2) ; reflection in the y-axis ; centre (0, 0), 90° anticlockwise ; (2, 2), (6, 2), (2, 4)

Activity 4: 2.5 ; 15 cm ; 12 cm ; 2/3

Activity 5: Congruent ; similar but not congruent ; similar but not congruent ; neither (the side ratios are not equal: 6/3 = 2, but 11/5 = 2.2)