GEOM A - Triangle Congruence by ASA and AAs answers to all questions
1) State the ASA congruence postulate.
The ASA congruence postulate states that if two angles and their included side of one triangle are congruent to two angles and their included side of another triangle, then the two triangles are congruent.
2) State the AAS congruence theorem.
The AAS congruence theorem states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.
3) Are two triangles congruent if they have two congruent sides and one congruent angle that is not included between the two sides?
No, two triangles are not congruent if they have two congruent sides and one congruent angle that is not included between the two sides. This is because the SSA (Side-Side-Angle) condition does not guarantee congruence. There can be multiple triangles with the same side lengths and angles that are not congruent.
4) Can two triangles be congruent if they have two congruent angles and a non-included side that is congruent?
No, two triangles cannot be congruent if they have two congruent angles and a non-included side that is congruent. This condition does not guarantee congruence as there can be multiple triangles with the same angle measures and side lengths that are not congruent.
5) Can two triangles be congruent if they have two congruent sides and one congruent angle that is included between the two sides?
Yes, two triangles can be congruent if they have two congruent sides and one congruent angle that is included between the two sides. This is the ASA (Angle-Side-Angle) condition for congruence.
6) Can two triangles be congruent if they have two congruent angles and a non-included side that is proportional?
No, two triangles cannot be congruent if they have two congruent angles and a non-included side that is proportional. The proportional side does not guarantee congruence as there can be multiple triangles with the same angle measures and proportional side lengths that are not congruent.