SAS CONGRUENCY POSTULATE
Definition Of SAS Congruency Postulate
SAS postulate states, "If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent."
More About SAS Congruency Postulate
The angle between any two sides of a triangle is called the included angle of the triangle.
Video Examples: SAS Triangle Congruence Postulate Explained
Example of SAS Congruency Postulate
In the figures shown, it is clear that two sides and one angle of these triangles are same. So, by SAS postulate these two triangles are congruent.
Solved Example on SAS Congruency Postulate
Ques: 
and m∠B = m∠Q. What additional information is required to prove that ΔABC ≅ ΔPQR by the SAS postulate?
Choices:
Correct Answer: A
Solution:
Step 1: If two sides and the included angle of one triangle a
re congruent to two sides and the included angle of another triangle,
then the two triangles are congruent. [SAS Postulate.]
Step 2: Hence, 
, then by the SAS postulate, ΔABC ≅ ΔPQR.
Quick Summary
- SAS stands for Side-Angle-Side.
- The angle must be *included* between the two sides.
- If SAS conditions are met, triangles are congruent.
⚠️ Common Mistakes
- Confusing SAS with other congruence postulates (e.g., ASA, SSS).
- Not verifying that the angle is *included* between the two sides.
🌍 Real-World Uses
- Construction: Ensuring the structural integrity of trusses in bridges by guaranteeing that triangles with specific side and angle measurements are congruent, leading to predictable load distribution.
- Engineering: Designing airplane wings where sections need to be identical for balance and performance, relying on SAS to ensure uniformity in manufactured parts.
- Navigation: Using triangulation with known distances and included angles to determine location, relying on SAS congruence to accurately map positions.
📋 Standards Alignment
CCSS.MATH.CONTENT.HSG.CO.B.8
🔗 Related Links
🍎 Teacher Insights
Use visual aids and hands-on activities to demonstrate the postulate. Provide plenty of examples and non-examples to highlight the importance of the included angle.🎓 Prerequisites
- Basic triangle properties
- Congruence
- Angles and sides of a triangle
Check Your Knowledge
Q1: Which of the following conditions proves triangle congruence by SAS?
Frequently Asked Questions
Q: What does 'included angle' mean?
A: The included angle is the angle formed by the two sides being considered.
Q: Does the order of 'Side-Angle-Side' matter?
A: Yes, the angle MUST be between the two sides.