ANGLE SIDE ANGLE CONGRUENCY

Angle-Angle-Side Congruency

Definition Of Angle Side Angle Congruency

ASA congruence postulate states that if two angles and the included side of one triangle are congruent to the two angles and the included side of another triangle, then the two triangles are congruent.

Examples of Angle Side Angle Congruency

exAngle Side Angle Congruencyple of Angle Side Angle Congruency

If ∠P≅∠T, and ≅, and ∠S≅∠R, then ΔPQS≅ΔQRT.

Video Examples: ASA (Angle-Side-Angle) Congruence rule and Proof

Solved Example Clockple on Angle Side Angle Congruency

Ques: Which of the figures satisfies the ASA congruence condition?

Angle Side Angle Congruencyple of Angle Side Angle Congruency

Choices:

A. Figure 2
B. Figure 1 and Figure 2
C. Figure 1
D. none of the above
Correct Answer: C

Solution:

Step 1: ASA congruence condition: If the measures of two angles and one side in a triangle are equal to the measures of corresponding two angles and one side of another triangle, then the two triangles are congruent.
Step 2: From Figure 1, AC = CD and∠A ≅∠D, ∠ACB≅∠DCE.
Step 3: ΔABC≅ΔDCE by ASA congruency condition
Step 4: From Figure 2, QR = RT, PR = RS and ∠PRQ ≅ ∠SRT
Step 5: ΔPQR ≅ ΔSRT by SAS congruency condition
Step 6: Only Figure 1 satisfies the ASA congruence condition.

Quick Summary

Two angles and the included side determine congruence.
ASA is a postulate, not a theorem.
ASA is different from AAS (Angle-Angle-Side).

\[ \triangle ABC \cong \triangle DEF \text{ if } \angle A \cong \angle D, \overline{AB} \cong \overline{DE}, \angle B \cong \angle E \]

🍎 Teacher Insights

Use visual aids and hands-on activities to demonstrate ASA. Emphasize the importance of the 'included side'. Compare and contrast with other congruence postulates (SSS, SAS, AAS).

🎓 Prerequisites

Basic triangle properties
Angle measurement
Side measurement
Congruence definition

Check Your Knowledge

Q1: Which of the following conditions proves triangle congruence by ASA?

Two sides and an included angle Two angles and an included side Three sides Two angles and a non-included side

Q2: If angle A is congruent to angle D, side AB is congruent to side DE, and angle B is congruent to angle E, are triangles ABC and DEF congruent?

Yes, by ASA Yes, by SAS Yes, by SSS No, not enough information

Frequently Asked Questions

Q: What does 'included side' mean?
A: The 'included side' is the side that lies between the two angles.

Q: Is ASA the same as AAS?
A: No, ASA requires the side to be *between* the two angles, while AAS has the side opposite one of the angles.