Discovering the Magic of ASA and AAS Congruence in Triangles

ASA proves two triangles congruent from two angles and the side between them. AAS uses two angles and a side that is not between them, and it works because knowing two angles fixes the third.

• Ensure you know the magnitudes of two angles and the length of the included side for both triangles.
• Compare these angles and the side.
• If both conditions are met, then the triangles are congruent.

• Make sure you know the magnitudes of two angles and the length of a side (that’s not between the two angles) for both triangles.
• Compare these angles and the side.
• If all match, then the triangles are congruent.

Worked examples: ASA and AAS congruence

Practice questions on ASA and AAS congruence

1. Are triangles with angles (60^{circ}) and (80^{circ}), and a non-included side of (10 text{ cm}), and another triangle with angles (60^{circ}) and (80^{circ}), with a non-included side of (11 text{ cm}) congruent by the AAS postulate?
2. Are triangles with angles (70^{circ}) and (110^{circ}), and an included side of (12 text{ cm}), and another triangle with angles (70^{circ}) and (110^{circ}), with an included side of (12 text{ cm}) congruent by the ASA postulate?

1. No
2. Yes

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