Master the Triangle Inequality Theorem with this comprehensive, no-prep geometry worksheet pack! Perfect for KS3 and KS4 math lessons, homework, or cover work. Students will practice checking valid side lengths, calculating the range for a missing third side, and ordering sides based on angle sizes. Includes full, step-by-step solutions!

Looking for a rigorous, no-prep math resource to help your students master side-length relationships in triangles?
This highly focused geometry topic pack is designed to help students build a solid conceptual and mathematical understanding of triangle inequalities. Whether you need a structured cover lesson, targeted homework, classroom practice, or an all-in-one exam revision worksheet, this resource is ready to print and go!
Every question comes paired with complete, fully worked step-by-step solutions, making grading an absolute breeze and allowing students to peer-mark or self-assess effectively.

What Skills Are Covered?
• Triangle Feasibility Rules: Deciding whether a given set of three numbers can successfully form a geometric triangle.
• Applying the Theorem: 91¶¶Òõting the rule that the sum of any two sides must be strictly greater than the remaining side to prove or disprove a triangle’s existence.
• Finding the Missing Third Side Range: Calculating between which two numeric values a missing third side must fall given two known side measurements (e.g., using difference and sum limits).
• Side-Angle Inequalities: Comparing and ordering the side lengths of isosceles or scalene triangles by evaluating their opposite interior angles (incorporating the 180-degree triangle angles rule).

Why Teachers Choose This Resource Pack:
• Zero Prep Needed: Just download, print, and you are ready to go!
• Step-by-Step Solutions: Complete answer keys show the geometric logic behind every range and restriction, not just a final number.
• Scaffolded Practice: Moves seamlessly from basic side checking to multi-step logic and angle-to-side comparisons.
• Clean Layout: Minimalist design ensures a clean presentation, reducing distractions for focused, stress-free student learning.

Curriculum Alignment:
• Key Stage 3 & Key Stage 4 (KS3/KS4): Ideal for Core Geometry and Measures strands.
• Target Groups: Perfect for Year 8, Year 9, and Year 10 students preparing for GCSE and IGCSE foundation or higher tier topics.