Respuesta :

LadyStrange

Direct answer :

[tex]\color{plum}\boxed{\tt Statements : }[/tex]

  1. Segment AB = Segment AD
  2. Segment BC = Segment DC
  3. Angle B and Angle D are equal.
  4. Segment AC bisects angle BAD
  5. Segment AC = Segment AC
  6. ∠ACD = ∠ACB
  7. △ABC≅△ADC under ASA congruence criterion.
  8. △ABC≅△ADC under SAS congruence criterion.

[tex]\color{plum}\boxed{ \: \tt Reasons : }[/tex]

  1. It is given.
  2. It is given.
  3. It is given. They are also equal because the bisector AC bisects angle BAD and divides it into two equal angles which are angle B and angle D.
  4. It is given.
  5. Common side.
  6. Common angle.
  7. Two angles and one included side is equal so these two triangles are congruent under the ASA congruence criterion.
  8. Two sides and one included side is equal so these two triangles are congruent under the SAS congruence criterion as well.

Steps to derive these statements and reasons :

Given :

  • segment AB = segment AD
  • segment BC = segment DC
  • ∠B =∠D
  • segment AC bisects ∠BAD

This means that △ABC≅△ADC under the SAS congruence criterion because according to this criterion if two sides and one included angle is equal two triangles are congruent and since these two triangles fulfill these rules they are said to be congruent under the SAS congruence criterion. But they are also congruent under the ASA congruence criterion which states that if two angles and one included side is equal two triangles are congruent. Since △ABC and △ADC fulfill these rules too they can said to be congruent under the ASA congruence criterion.

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