One Unique Triangle, Many or None - Notes and Practice

Determine whether three given side lengths can form a triangle using the Triangle Inequality Theorem.

Find a missing interior angle of a triangle using the Triangle Angle Sum Theorem.

Classify a set of side lengths or angle measures as producing one unique triangle, many triangles, or no triangle.

Have students shade the true/false warm-up on the first notes page before instruction, then revisit it with the answer key afterward per the two suggested usage options printed in the file.

Use the linked Google Forms version of the Triangles Test Practice for a self-grading digital assessment instead of the printable version.

Consider the two separately available 'hands-on activity' resources referenced in the file (Triangle Inequality and Triangle Angle Sum explorations) before these notes if students haven't yet built intuition for the theorems.

Triangle Inequality Theorem application -- students test whether three given side lengths (e.g., 9 in, 13 in, 5 in) can form a triangle by checking that the two shorter sides sum to more than the longest.

Triangle Angle Sum Theorem application -- students solve for a missing interior angle given two known angles, using the fact that all three sum to 180°.

Triangle classification -- students determine whether a set of measurements produces one unique triangle, many triangles, or no triangle, applying both theorems together.