Tessellations & Triangles: Angles Worksheets is a hands-on and reasoning-rich resource that helps students prove through exploration that all triangles can tessellate. By measuring, drawing and analysing internal angles, students develop geometric fluency and gain a deeper understanding of how shapes combine to fill space. This task brings mathematical theory to life through creative investigation and visual patterning.

Students begin by reviewing the angle properties of triangles, measuring internal angles and calculating the total. They then use these measurements to experiment with how different types of triangles, equilateral, isosceles and scalene, can tessellate without leaving gaps. The final section prompts students to reflect and compare triangle tessellations with other shapes, reinforcing the geometric concept that all triangles, regardless of type, can tessellate.

This activity is ideal for upper primary or lower secondary students and works well during a unit on angles, shape properties or transformation. Whether used in a whole-class lesson or as part of a small-group maths rotation, it supports a blend of mathematical reasoning, drawing accuracy and pattern creation. It also provides a meaningful context for vocabulary development and for making connections between abstract angle rules and visual outcomes.

Key Learning Outcomes:

• ✅ Measure and calculate internal angles of triangles
• ✅ Use angle sums to prove tessellation patterns
• ✅ Apply geometric reasoning to justify tessellation behaviour
• ✅ Identify and describe different triangle types
• ✅ Develop spatial awareness and visual patterning skills

What’s Included:

• Worksheets focused on triangle measurement and tessellation
• Tasks for measuring, calculating, and recording internal angle sums
• Drawing sections for students to create triangle tessellations
• Reflection task to support reasoning and shape comparison

Materials Needed:

• Printed worksheets
• Pencils and erasers
• Rulers and protractors for angle measurement
• Coloured pencils or markers for pattern design

How to Use:

• Begin with a class discussion on the internal angles of triangles (sum = 180°)
• Guide students to measure angles on different triangle types and record their findings
• Have students experiment with drawing repeating triangle patterns to test for tessellation
• Support reflection by comparing triangle tessellations to those of other polygons
• Discuss why all triangles tessellate, using angle reasoning and visual examples

Ideas for Classroom Use:

• 💡 Use during a geometry unit to explore angle properties and shape behaviour
• 💡 Set up as a station with triangle tiles and drawing tools for hands-on exploration
• 💡 Incorporate into a cross-curricular lesson linking maths with art or architecture
• 💡 Have students present their tessellations and explain the reasoning behind them

Top Teacher Tips:

• 💛 Encourage students to label each triangle type clearly for comparison
• 💛 Provide stencils or tracing paper for support with accurate drawing
• 💛 Use anchor charts or posters to reinforce vocabulary such as “revolution,” “tessellate,” and “angle sum”
• 💛 Link to real-world examples of tessellations using triangles in cultural and architectural design

Tessellations & Triangles: Angles Worksheets empowers students to explore mathematical concepts through investigation and creativity. By working through measurements, constructing patterns, and justifying their conclusions, students gain confidence and a deeper understanding of angles and spatial structure.