What does the SAS Congruence Theorem say?(1 point)
Responses
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 a triangle has an angle between two congruent sides, then it is isosceles.
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 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.
The correct response is:
"If two triangles have one pair of congruent angles and one pair of congruent sides, then the triangles are congruent."
The correct statement of the SAS Congruence Theorem is: "If two triangles have one pair of congruent angles between two pairs of congruent sides, then the triangles are congruent." This theorem states that if we have two triangles with one pair of congruent angles and one pair of congruent sides between those angles, then we can conclude that the two triangles are congruent. This means that all corresponding sides and angles of the two triangles are equal in measure.
To understand this theorem, we need to know what congruent means. Two figures are congruent if they have the same shape and size. In the case of triangles, congruence means that all corresponding sides and angles are equal.
To apply the SAS Congruence Theorem, we need to identify one pair of congruent angles between two pairs of congruent sides in the given triangles. If these conditions are met, we can conclude that the triangles are congruent. This theorem is useful in proving the congruence of triangles when we have specific information about their angles and sides.