Triangle Congruence: SAS Flashcards
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Questions and Answers

What is the missing statement in the proof that ΔACB ≅ ΔECD, given that AE and DB bisect each other at C?

∠ACB ≅ ∠ECD

Which of these triangle pairs can be mapped to each other using a single translation?

  • Triangle Pair A
  • Triangle Pair C
  • Triangle Pair D (correct)
  • Triangle Pair B
  • What is the second transformation used to map ΔHJK to ΔLMN after the translation of vertex H to vertex L?

    a rotation about point H

    Which of these triangle pairs can be mapped to each other using a single reflection?

    <p>Triangle Pair A</p> Signup and view all the answers

    Which of these triangle pairs can be mapped to each other using both a translation and a reflection across the line containing AB?

    <p>Triangle Pair D</p> Signup and view all the answers

    What additional information is needed to show ΔJKL ≅ ΔMNR by SAS, given that KL ≅ NR and JL ≅ MR?

    <p>∠L ≅ ∠R</p> Signup and view all the answers

    What is the missing statement in the proof that ΔEFG ≅ ΔJHG, given that G is the midpoint of HF, EF ∥ HJ, and EF ≅ HJ?

    <p>∠GFE ≅ ∠GHJ</p> Signup and view all the answers

    Can it be concluded that ΔRQS ≅ ΔNTV by SAS? Why or why not?

    <p>No, it is not possible for the triangles to be congruent.</p> Signup and view all the answers

    Segments _______ are therefore congruent by the definition of bisector.

    <p>MS and QS</p> Signup and view all the answers

    Which rigid transformation would map ΔAQR to ΔAKP?

    <p>a rotation about point A</p> Signup and view all the answers

    Study Notes

    Triangle Congruence: SAS

    • ΔACB ≅ ΔECD requires missing statement: ∠ACB ≅ ∠ECD for proof.
    • Identification of triangle pairs that can undergo a single translation, specifically D.
    • Mapping ΔHJK to ΔLMN involves two rigid transformations; first is translation from H to L, second is a rotation about point H.
    • Determination of triangle pairs that can be mapped using a single reflection indicates pair A.
    • Analysis reveals that pair D cannot be mapped through both translation and reflection across line AB.
    • To show ΔJKL ≅ ΔMNR by SAS with given KL ≅ NR and JL ≅ MR, additional requirement is ∠L ≅ ∠R.
    • For congruence of ΔEFG and ΔJHG, missing proof component is ∠GFE ≅ ∠GHJ, stated within the isosceles context.
    • Triangles RQS and NTV have right angles at ∠Q and ∠T respectively, but due to lacking necessary congruence, ΔRQS ≅ ΔNTV cannot be concluded by SAS.
    • Proof context of isosceles triangle ΔMNQ highlights base angles’ congruence; segments MS and QS must be congruent due to bisector definition.
    • Rigid transformation mapping ΔAQR to ΔAKP requires a rotation about point A for accurate congruence alignment.

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    Test your understanding of triangle congruence with these flashcards focusing on the Side-Angle-Side (SAS) theorem. Each card presents a challenge related to triangle proofs and transformations. Perfect for reinforcing concepts in geometry.

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