Discovering the Magic of ASA and AAS Congruence in Triangles
- 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.
Examples
Practice Questions:
- 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?
- 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?
- No
- Yes
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