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?
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?
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Which of these triangle pairs can be mapped to each other using both a translation and a reflection across the line containing AB?
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What additional information is needed to show ΔJKL ≅ ΔMNR by SAS, given that KL ≅ NR and JL ≅ MR?
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What is the missing statement in the proof that ΔEFG ≅ ΔJHG, given that G is the midpoint of HF, EF ∥ HJ, and EF ≅ HJ?
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Can it be concluded that ΔRQS ≅ ΔNTV by SAS? Why or why not?
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Segments _______ are therefore congruent by the definition of bisector.
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Which rigid transformation would map ΔAQR to ΔAKP?
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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.
