Question

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

Answer 1

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 ACD

Answer: Fourth option AB=AD

Answer 2

AB ≅ AD.

Further explanation

• We observe that both the ABC triangle and the ADC triangle have the same AC side length. Therefore we know that $\boxed{ \ \overline{AC} \cong \overline{AC} \ }$ is reflexive.
• Furthermore, both triangles have equal angles, i.e., ∠BAC = ∠DAC.
• In order to prove the triangles congruent using the SAS congruence postulate, we need the additional information, namely $\boxed{ \ \overline{AB} \cong \overline{AD} \ }$.

Conclusions for the SAS Congruent Postulate from this problem:

• $\boxed{ \ \overline{AC} = \overline{AC} \ }$
• ∠BAC = ∠DAC
• $\boxed{ \ \overline{AB} = \overline{AD} \ }$

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The following is not other or additional information along with the reasons.

• ∠CBA = ∠CDA no, because that is AAS with ∠ACB = ∠ACD and $\boxed{ \ \overline{AC} \cong \overline{AC} \ }$

• ∠BAC = ∠DAC no, because already marked.

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Notes

• The SAS (Side-Angle-Side) postulate for the congruent triangles: two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle; the included angle properly represents the angle formed by two sides.
• The ASA (Angle-Side-Angle) postulate for the congruent triangles: two angles and the included side of one triangle are congruent to two angles and the included side of another triangle; the included side properly represents the side between the vertices of the two angles.  
• The SSS (Side-Side-Side) postulate for the congruent triangles: all three sides in one triangle are congruent to the corresponding sides within the other.
• The AAS (Angle-Angle-Side) postulate for the congruent triangles: two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.  

Learn more

1. Which shows two triangles that are congruent by ASA?  https://brainly.com/question/8876876  
2. Which shows two triangles that are congruent by AAS https://brainly.com/question/3767125
3. What other information do you need in order to prove the triangles congruent using the SAS congruence postulate? https://brainly.com/question/2644126