What you’ll learn
Determine congruence using rigid motions.
Key idea
A composition of rigid motions preserves all lengths and angle measures; orientation reversal does not prevent congruence.
Composition of rigid motions preserves corresponding lengths and angles even when orientation reverses.
Worked example
Enter the exact value or ordered values in the format requested below.
Triangle ABC is reflected, then translated. Original AB=2.6 cm. Enter corresponding image A'B' length and unit.
- Reflection preserves the length of corresponding side AB=2.6 cm, even though vertex orientation reverses.
- The following translation also preserves lengths and angles; image and original side therefore both measure 2.6 cm and triangles are congruent.
Answer: 2.6 cm
Quick Check
Evaluate a worked attempt at determine congruence using rigid motions, identify the first invalid step, and provide the correction.
Triangle side AB=5.1 cm is reflected then translated. Step 1 notes reflection reverses vertex orientation. Step 2 claims the triangles cannot be congruent solely because of reversed orientation. Identify the first invalid step and correct it with corresponding-length evidence.