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IgorC [24]
3 years ago
13

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

Mathematics
2 answers:
iren [92.7K]3 years ago
9 0

AC is perpendicular to BD.

<h3>Further explanation</h3>
  • 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} \ }

- - - - - - - - - -

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.

- - - - - - - - - -

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.  
<h3>Learn more</h3>
  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  
sergij07 [2.7K]3 years ago
3 0
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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