What does the SAS Congruence Theorem say?(1 point)
Responses
If two triangles have one pair of congruent angles and two pairs of congruent sides, then the triangles are congruent.
If two triangles have one pair of congruent angles and two pairs of congruent sides, then the triangles are congruent.
If two triangles have one pair of congruent angles and at least one pair of congruent sides, then the triangles are congruent.
If two triangles have one pair of congruent angles and at least one pair of congruent sides, then the triangles are congruent.
If two triangles have one pair of congruent angles between two pairs of congruent sides, then the triangles are congruent.
If two triangles have one pair of congruent angles between two pairs of congruent sides, then the triangles are congruent.
If a triangle has an angle between two congruent sides, then it is isosceles.
If two triangles have one pair of congruent angles between two pairs of congruent sides, then the triangles are congruent.
The correct answer is: If two triangles have one pair of congruent angles and two pairs of congruent sides, then the triangles are congruent.
The correct statement of the SAS (Side-Angle-Side) Congruence Theorem is: "If two triangles have one pair of congruent angles and two pairs of congruent sides, then the triangles are congruent."
To explain how to arrive at this answer, you need to understand the concept of congruent triangles and how the SAS Congruence Theorem is applied.
First, two triangles are said to be congruent if all their corresponding sides and angles are equal in measure. This means that for two triangles to be congruent, their corresponding angles and sides must have the same measures.
The SAS Congruence Theorem states that if two triangles have one pair of congruent angles and two pairs of congruent sides, then the triangles are congruent.
To prove the congruence of triangles using the SAS Congruence Theorem, you need to ensure that:
1. One pair of angles in both triangles are congruent.
2. Two pairs of sides in both triangles are congruent.
If these conditions are met, you can conclude that the two triangles are congruent.