The postulates of congruent triangles and the congruence criteria of SAS, ASA, SSS, and AAS are all related to the concept of congruent triangles. The postulates are used to prove that two triangles are congruent, while the congruence criteria are used to show that two triangles are congruent based on the given information.
The postulates of congruent triangles state that:
1.Side-Side-Side (SSS) Postulate: If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
2.Side-Angle-Side (SAS) Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
3.Angle-Side-Angle (ASA) Postulate: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
4.Angle-Angle-Side (AAS) Congruence: 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
The difference between the postulates and the congruence criteria lies in the information given. The postulates assume that all three sides or angles of two triangles are congruent, while the congruence criteria provide specific information about the sides and angles that are congruent
Answers & Comments
Answer:
The postulates of congruent triangles and the congruence criteria of SAS, ASA, SSS, and AAS are all related to the concept of congruent triangles. The postulates are used to prove that two triangles are congruent, while the congruence criteria are used to show that two triangles are congruent based on the given information.
The postulates of congruent triangles state that:
1.Side-Side-Side (SSS) Postulate: If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
2.Side-Angle-Side (SAS) Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
3.Angle-Side-Angle (ASA) Postulate: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
4.Angle-Angle-Side (AAS) Congruence: 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
The difference between the postulates and the congruence criteria lies in the information given. The postulates assume that all three sides or angles of two triangles are congruent, while the congruence criteria provide specific information about the sides and angles that are congruent
✏️ANSWER:
1. SAS ( side, angle, side )
2. ASA ( angle, side, angle )
3. SSS ( side, side, side )
4. AAS ( angle, angle, side )
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