Question

What other information do you need in order to prove the triangles congruent using the SAS congruence postulate

Answer 1

AC is perpendicular to BD.

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.
• The length of the base of the triangle is the same, i.e., $\boxed{ \ \overline{BC} = \overline{CD} \ }$.
• In order to prove the triangles congruent using the SAS congruence postulate, we need the other information, namely $\boxed{ \ AC \bot BD \ }$. Thus we get ∠ACB = ∠ACD = 90°.

Conclusions for the SAS Congruent Postulate from this problem:

• $\boxed{ \ \overline{BC} = \overline{CD} \ }$
• ∠ACB = ∠ACD
• $\boxed{ \ \overline{AC} = \overline{AC} \ }$

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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 that is ASA with $\boxed{ \ \overline{AC} \cong \overline{AC} \ }$ and ∠ACB = ∠ACD.
• $\boxed{ \ \overline{BC} = \overline{CD} \ }$ 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?  brainly.com/question/8876876  
2. Which shows two triangles that are congruent by AAS brainly.com/question/3767125
3. About vertical and supplementary angles brainly.com/question/13096411  

Answer 2

A SAS congruence postulate means that it must have an equal side,angle,side! so in this example, it tells us a side that's equal so you'd need to prove an angle and another side to prove the triangles congruent
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