Congruent Triangles Worksheet

Congruent triangles at a glance

Congruent triangles are triangles which are exactly the same. If two triangles are congruent, all of their sides and angles are the same as each other. There are four ways to prove triangle congruence. These are:

ASA – if you can show that two sides and the angle between them are the same in both triangles, they must be congruent
SAS – if you can show that two angles and the side between them are the same in both triangles they must be congruent
SSS – if all three sides of the triangles are the same, they are congruent
RHS – if the triangles are right angle triangles with equal hypotenuses and one other equal side, they must be congruent

Take a parallelogram, ABCD where AC and BD are opposing vertices and the diagonal AC is connected, triangulating the parallelogram.

Triangle ABC and triangle ADC are a pair of congruent triangles. Since opposite sides in a parallelogram are equal, BC and AD are corresponding sides in the two triangles. The triangles also share the side AC, the diagonal of the parallelogram. Finally, angles BCA and CAD are alternate angles meaning they are equal. The triangles are congruent by SAS. 

When proving congruence, we often need to use a variety of angle facts to identify whether angles are equal. These angle facts might  include angles in a triangle, angles in parallel lines and circle theorems. 

Looking forward, students can then progress to additional geometry worksheets, for example a simplifying expressions worksheet or simultaneous equations worksheet.

For more teaching and learning support on Geometry our GCSE maths lessons provide step by step support for all GCSE maths concepts.