Mathematics

Question

The proof shows that opposite angles of a parallelogram are congruent. Given: ABCD is a parallelogram with diagonal AC. Prove: ∠ BAD ≅ ∠ DCB What is the missing reason In this partial proof? Question 3 options:
ASA Substution Angle Angle Postulate Alternate Interior Angles are Congruent

1 Answer

  • A parallelogram is a figure which has its opposite sides to be equal and parallel. The missing reason in the proof is:

    B. Substitution Angle Angle Postulate.

    A parallelogram is a type of quadrilateral that has its opposite sides to be equal and parallel. The sum of its internal angles is [tex]360^{o}[/tex].

    To prove that ∠ BAD ≅ ∠ DCB, we have:

    Given parallelogram ABCD;

    <BAC ≅ <ACD (alternate angle theorem)

    <DAC ≅ <ACB (alternate angle theorem)

    <BAC + <DAC = <BAD

    Also,

    <BCA + <DCA = <BCD

    Therefore,

    <BAD ≅ <DCB (Substitution Angle Angle Postulate)

    Thus, the missing reason in the partial proof is:

    option B. Substitution Angle Angle Postulate

    A sketch is attached to this question for more clarifications.

    Visit: https://brainly.com/question/3100335

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