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6. determine the relationship between the two triangles and whether or …

Question

  1. determine the relationship between the two triangles and whether or not they can be proven to be congruent.

the two triangles are related by
\underline{\hspace{3cm}}^{word bank 1}, so the triangles
\underline{\hspace{3cm}}^{word bank 2}.

  1. determine the relationship between the two triangles and whether or not they can be proven to be congruent.

the two triangles are related by
\underline{\hspace{3cm}}^{word bank 1}, so the triangles
\underline{\hspace{3cm}}^{word bank 2}.

  1. determine the relationship between the two triangles and whether or not they can be proven to be congruent.

the two triangles are related by
\underline{\hspace{3cm}}^{word bank 1}, so the triangles
\underline{\hspace{3cm}}^{word bank 2}.

  1. determine the relationship between

and whether or not they can be proven to be
the two triangles are related by
\underline{\hspace{3cm}}^{word bank 1}, so the triangles
\underline{\hspace{3cm}}^{word bank 2}.

  1. determine the relationship between the two triangles and whether or not they can be proven to be congruent.

the two triangles are related by
\underline{\hspace{3cm}}^{word bank 1}, so the triangles
\underline{\hspace{3cm}}^{word bank 2}.

  1. determine the relationship between the two triangles and whether or not they can be proven to be congruent.

the two triangles are related by
\underline{\hspace{3cm}}^{word bank 1}, so the triangles
\underline{\hspace{3cm}}^{word bank 2}.

Explanation:

Brief Explanations

For each problem, identify the triangle congruence criterion (ASA, SAS, AAS, SSS) based on marked sides/angles, then state if they are congruent.

  1. Problem 6: Two pairs of congruent angles and one pair of congruent included sides match the ASA (Angle-Side-Angle) criterion, which proves congruence.
  2. Problem 7: Two pairs of congruent sides and one pair of congruent included angles match the SAS (Side-Angle-Side) criterion, which proves congruence.
  3. Problem 8: Two pairs of congruent angles and one pair of congruent non-included sides match the AAS (Angle-Angle-Side) criterion, which proves congruence.
  4. Problem 9: Two pairs of congruent sides and one pair of congruent non-included angles is SSA, which does not prove congruence.
  5. Problem 10: Two pairs of congruent angles and one pair of congruent non-included sides match the AAS (Angle-Angle-Side) criterion, which proves congruence.
  6. Problem 11: All three pairs of corresponding sides are congruent, matching the SSS (Side-Side-Side) criterion, which proves congruence.

Answer:

  1. The two triangles are related by ASA (Angle-Side-Angle), so the triangles can be proven congruent.
  2. The two triangles are related by SAS (Side-Angle-Side), so the triangles can be proven congruent.
  3. The two triangles are related by AAS (Angle-Angle-Side), so the triangles can be proven congruent.
  4. The two triangles are related by SSA (Side-Side-Angle), so the triangles cannot be proven congruent.
  5. The two triangles are related by AAS (Angle-Angle-Side), so the triangles can be proven congruent.
  6. The two triangles are related by SSS (Side-Side-Side), so the triangles can be proven congruent.