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Complete the proof given below.

Given: ABCD is a parallelogram

Prove: ∠BCA≅∠DAC


ABCD is a parallelogram=
AB≅DC, BC≅AD=
AC≅AC=
△ABC≅△CDA=
∠BCA≅∠DAC=
(Choices V)
SSS Given Sas Reflexive property Definition of congruent SSA ABCD IS A PARALLELOGRAM Transitive property ASA CPCTC
WILL GIVE 35 POINTS

Sagot :

Given that the opposite sides of a parallelogram are congruent, a diagonal

of the parallelogram forms two congruent triangles.

The correct options to complete the proof are;

  • Opposite sides of a parallelogram; ABCD is a parallelogram
  • Reflexive property of congruency
  • SSS

Reasons:

The completed two column proof is presented as follows;

Statement  [tex]{}[/tex]                                  Reason

1. ABCD is a parallelogram  [tex]{}[/tex]       1. Given

2. [tex]\overline{AB}[/tex] ≅ [tex]\overline{DC}[/tex] and [tex]\overline{BC}[/tex] ≅ [tex]\overline{DA}[/tex]  [tex]{}[/tex]      2. Opposite sides of a parallelogram

3. [tex]\overline{AC}[/tex] ≅ [tex]\overline{CA}[/tex]    [tex]{}[/tex]                             3. Reflexive property of congruency

4. ΔABC ≅ ΔCDA     [tex]{}[/tex]                   4. SSS

The correct options are therefore;

Opposite sides of a parallelogram; ABCD is a parallelogram

Reflexive property of congruency

SSS;

Reason 2. Opposite sides of a parallelogram, which is based on the

properties of a parallelogram and that ABCD is a parallelogram.

Reason 3. The reflexive property of congruency, states that a side is

congruent to itself.

Reason 4. SSS is an acronym for Side-Side-Side, which is a congruency

postulate that states that if the three sides of one triangle are equal to the

three sides of another triangle, then the two triangles are congruent.

Learn more about parallelograms here:

https://brainly.com/question/4218263

https://brainly.com/question/21390857

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