MATH SOLVE

2 months ago

Q:
# What additional information is needed to prove that triangles are congruent by the SAS Postulate?

Accepted Solution

A:

Answer: Fourth Option AB=AD

Solution:The SAS (Side Angle Side) Postulate indicates that two triangles are congruent if they have two congruent sides and congruent the angle between these sides.According with the figure, the triangles ABC and ACD have a congruent side (S) AC, because is a common side between the two triangles.Additionally they have a congruent angle (A): the angle BAC in triangle ABC is congruent with the angle DAC in triangle ACD (indicated in the figure).Then we have one congruent side (S) and one congruent angle (A). We need another congruent side to complete the SAS postulate:The side (S) AB in triangle ABC must be congruent with the side AD in triangle ACDAnswer: Fourth option AB=AD

Solution:The SAS (Side Angle Side) Postulate indicates that two triangles are congruent if they have two congruent sides and congruent the angle between these sides.According with the figure, the triangles ABC and ACD have a congruent side (S) AC, because is a common side between the two triangles.Additionally they have a congruent angle (A): the angle BAC in triangle ABC is congruent with the angle DAC in triangle ACD (indicated in the figure).Then we have one congruent side (S) and one congruent angle (A). We need another congruent side to complete the SAS postulate:The side (S) AB in triangle ABC must be congruent with the side AD in triangle ACDAnswer: Fourth option AB=AD