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NOTE: On the bottom right corner of each question, you will see a button that says “Check Answer.” Click this to check your answer before submitting. It will not tell you the correct answer, but it will tell you whether the answer you selected is correct or not. You can use this feature ONCE per question (only for Quizzes and Sample Works). TaLynn was given two generic triangles with three pairs of congruent sides. She shows that a sequence of rigid transformations maps one triangle onto the other triangle such that the triangles overlap perfectly. What theorem was TaLynn justified through this process? (1 point) Responses the HL Congruence Theorem the HL Congruence Theorem the CPCTC Theorem the CPCTC Theorem the SAS Congruence Theorem the SAS Congruence Theorem the SSS Congruence Theorem the SSS Congruence Theorem Skip to navigation

6 answers

NOTE: On the bottom right corner of each question, you will see a button that says “Check Answer.” Click this to check your answer before submitting. It will not tell you the correct answer, but it will tell you whether the answer you selected is correct or not. You can use this feature ONCE per question (only for Quizzes and Sample Works). TaLynn was given two generic triangles with three pairs of congruent sides. She shows that a sequence of rigid transformations maps one triangle onto the other triangle such that the triangles overlap perfectly. What theorem was TaLynn justified through this process? (1 point) Responses the HL Congruence Theorem the HL Congruence Theorem the CPCTC Theorem the CPCTC Theorem the SAS Congruence Theorem the SAS Congruence Theorem the SSS Congruence Theorem the SSS Congruence Theorem Skip to navigation

The correct theorem that TaLynn was justified through this process is the SSS Congruence Theorem. This theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. Since TaLynn showed that there are three pairs of congruent sides, the SSS Congruence Theorem applies.

NOTE: On the bottom right corner of each question, you will see a button that says “Check Answer.” Click this to check your answer before submitting. It will not tell you the correct answer, but it will tell you whether the answer you selected is correct or not. You can use this feature ONCE per question (only for Quizzes and Sample Works). Are the triangles congruent? If so, write a congruence statement and reason why. (1 point) Responses No, the triangles are not congruent. No, the triangles are not congruent. Yes, △ABC≅△EFD by the SAS Congruence Theorem. Yes, △ABC≅△EFD by the SAS Congruence Theorem. Yes, △ABC≅△EFD by the SSS Congruence Theorem. Yes, △ABC≅△EFD by the SSS Congruence Theorem. Yes, △ABC≅△DEF by the SAS Congruence Theorem. Yes, △ABC≅△DEF by the SAS Congruence Theorem. Skip to navigation page 3 of 3

To determine whether the triangles are congruent, you would need to compare their corresponding angles and sides. However, since I don’t have the visual information to assess the triangles' measurements, I can't definitively say whether they are congruent or not, nor can I provide a specific congruence statement or theorem as rationale.

Generally:

  • If you know that two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, you can state "Yes, △ABC≅△DEF by the SAS Congruence Theorem."
  • If all three sides of one triangle are congruent to all three sides of another triangle, you might state, "Yes, △ABC≅△DEF by the SSS Congruence Theorem."
  • If there is not enough information to compare angles and sides, or if they do not match in these aspects, you would say, "No, the triangles are not congruent."

Please check the triangles' measurements and relationships to select the correct answer from the options provided.

NOTE: On the bottom right corner of each question, you will see a button that says “Check Answer.” Click this to check your answer before submitting. It will not tell you the correct answer, but it will tell you whether the answer you selected is correct or not. You can use this feature ONCE per question (only for Quizzes and Sample Works). If point C is the midpoint of both BD¯¯¯¯¯¯¯¯ and AE¯¯¯¯¯¯¯¯ , what additional information would you need to be able to state that △ABC≅△EDC by the SSS Congruence Theorem? (1 point) Responses AE¯¯¯¯¯¯¯¯≅DB¯¯¯¯¯¯¯¯ line segment cap A cap e is congruent to line segment cap d cap b ∠ACB≅∠ECD ∠ACB≅∠ECD B¯¯¯¯¯¯¯¯≅ED¯¯¯¯¯¯¯¯ line segment cap A cap b is congruent to line segment cap e cap d BC¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ line segment cap b cap c is congruent to line segment cap d cap c Skip to navigation

To state that \( \triangle ABC \cong \triangle EDC \) by the SSS Congruence Theorem, you would need to confirm that all three sides of one triangle are congruent to all three sides of the other triangle.

Since point C is the midpoint of both \( \overline{BD} \) and \( \overline{AE} \), you already know that \( AC \) and \( EC \) are congruent to half of \( AE \) and \( BD \), respectively. Therefore, you would need to establish the congruence of the third pair of sides, which in this case would involve proving one of the following pairs of sides congruent:

  • Option: \( BC \cong DC \) (which denotes that the length of segment \( BC \) is equal to the length of segment \( DC \)).

Thus, the best response would be:

BC¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ (line segment \( \overline{BC} \) is congruent to line segment \( \overline{DC} \)).

This information, along with the congruences of the other pairs derived from the midpoint, would justify the use of the SSS Congruence Theorem.