ANGLE ANGLE SIDE CONGRUENCY
Definition Of Angle Angle Side Congruency
Angle-Angle-Side (AAS) theorem states that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of another triangle, then the two triangles are congruent.
Examples of Angle Angle Side Congruency
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∠L = ∠P = 450, ∠M = ∠Q = 1100, MN = QR = 12 m
The two angles and non-included side of â–³LMN are equal to the corresponding angles and non-included side of â–³PQR. So, both the triangles are congruent.
Video Examples: AAS (Angle-Angle-Side) Congruence rule and Proof
Solved Example Clockple on Angle Angle Side Congruency
Ques: Find ∠D, if â–³ABC and â–³DEF are congruent by AAS property.
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Choices:
A. 220
B. 700
C. 1100
D. 480
Correct Answer: A
Solution:
Step 1: If two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of another triangle, then the two triangles are congruent. [AAS theorem]
Step 2: â–³ABC ≅ â–³DEF [Given]
Step 3: ∠B = ∠E = 1100 and AB = DE = 12 cm
Step 4: Since ∠C = 480, ∠F = 480 [â–³ABC and â–³DEF are congruent by AAS property.]
Step 5: ∠D + ∠E + ∠F = 1800 [Sum of the angles in a triangle is 1800.]
Step 6: ∠D + 1100 + 480 = 1800 [Substitute the values.]
Step 7: ∠D = 220
Quick Summary
- AAS Congruence Theorem states that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of another triangle, the triangles are congruent.
- AAS is a shortcut to prove triangle congruence without needing to show all sides and angles are congruent.
- It is important to identify the non-included side correctly to apply the theorem.
🍎 Teacher Insights
Use visual aids and interactive software to demonstrate the AAS theorem. Emphasize the difference between included and non-included sides. Provide plenty of practice problems where students have to identify congruent triangles using AAS.🎓 Prerequisites
- Understanding of angles and angle measurement
- Concept of triangle congruence
- Knowledge of corresponding parts of congruent triangles
- Basic algebraic manipulation
Check Your Knowledge
Q1: If in triangles ABC and DEF, ∠A ≅ ∠D, ∠B ≅ ∠E, and BC ≅ EF, are the triangles congruent?
Q2: Which of the following conditions is NOT sufficient to prove triangle congruence?
Frequently Asked Questions
Q: What is the difference between AAS and ASA?
A: In ASA, the side is included between the two angles, whereas in AAS, the side is not included between the two angles.
Q: Can I use AAS to prove triangles similar?
A: AAS proves congruence, which is a stricter condition than similarity. For similarity, you would typically use AA (Angle-Angle) similarity.