Triangles congruent by SAS and HL proofs

Triangles congruent by SAS and HL proofs

Lessons

  • 1.
    Write a two-column proof.
    a)
    Given: R is the midpoint of MP\overline {MP}.
    R is the midpoint of NQ\overline {NQ}.
    Prove: MRN\triangle MRN\congPRQ\triangle PRQ
    Proving triangles congruent by SAS and HL in a two-column proof

    b)
    Special case for right triangle:
    Given: ABC\triangle ABC is an isosceles triangle.
    D is the midpoint of AC\overline {AC}.
    Prove: ABD\triangle ABD\congCBD\triangle CBD.
    Proving triangles congruent by SAS and HL a two-column proof


  • 2.
    Write a flow proof
    a)
    Given: R is the midpoint of MP\overline {MP}.
    R is the midpoint of NQ\overline {NQ}.
    Prove: MRN\triangle MRN\congPRQ\triangle PRQ
    Triangles congruent by Side Angle Side and HL proofs

    b)
    Special case for right triangle:
    Given: ABC\triangle ABC is an isosceles triangle.
    D is the midpoint of AC\overline {AC}.
    Prove: ABD\triangle ABD\congCBD\triangle CBD.
    Triangles congruent by Side Angle Side and HL proofs


  • 3.
    Is there enough information given to prove the following triangles are congruent? If so, explain your reasoning and point out the theorem or postulate you use.
    a)

    Side Angle Side and HL proofs

    b)

    Triangles congruent by SAS and HL proofs