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BladeRunner212

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

Conclusions for the SAS Congruent Postulate from this problem:

  • [tex]\boxed{ \ \overline{BC} = \overline{CD} \ }[/tex]
  • ∠ACB = ∠ACD
  • [tex]\boxed{ \ \overline{AC} = \overline{AC} \ }[/tex]

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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 [tex]\boxed{ \ \overline{AC} \cong \overline{AC} \ }[/tex]
  • ∠BAC = ∠DAC no, because that is ASA with [tex]\boxed{ \ \overline{AC} \cong \overline{AC} \ }[/tex] and ∠ACB = ∠ACD.
  • [tex]\boxed{ \ \overline{BC} = \overline{CD} \ }[/tex] 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. About vertical and supplementary angles https://brainly.com/question/13096411  
ankitprmr2

If angle ABC and angle ADC are equal then the triangle ABC and triangle ADC is congruent by SAS.

Both the triangles have one side in common that is AC.

The length of the base of the triangle is the same, i.e. BC=CD.

In order to prove the triangles congruent using the SAS congruence postulate, we need the other information, likewise any of the angles that are equivalent in both the triangles. If angle ABC and angle ADC are equal then the triangle ABC and triangle ADC is congruent by SAS.

We required two sides and one angle equivalent in two triangles to prove these triangles are congruent by SAS axiom.

To know more about SAS congruence, please refer to the link:

https://brainly.com/question/1167632

 

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