ABC ARTL Write all 6 corresponding congruent statements by the Corresponding Parts of Congruent Thangles are Congruent (CPCTCY

Answer 1

When two triangles are proven to be congruent, their corresponding parts are also congruent according to the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) theorem. If we denote the triangles as \( \triangle ABC \) and \( \triangle ARTL \), the corresponding sides and angles can be expressed as follows:

1. Corresponding Angles:

   • \( \angle A \cong \angle A \)
   • \( \angle B \cong \angle R \)
   • \( \angle C \cong \angle T \)

2. Corresponding Sides:

   • \( AB \cong AR \)
   • \( BC \cong RT \)
   • \( CA \cong TL \)

So, the 6 corresponding congruent statements can be summarized as:

1. \( \angle A \cong \angle A \)
2. \( \angle B \cong \angle R \)
3. \( \angle C \cong \angle T \)
4. \( AB \cong AR \)
5. \( BC \cong RT \)
6. \( CA \cong TL \)

These statements indicate that each angle and each side of triangle ABC is congruent to the corresponding angle and side of triangle ARTL, following the principles of CPCTC once the triangles are established as congruent.

Answer 2

Simplify

Answer 3

Certainly! Here’s the simplified version of the corresponding congruent statements for triangles \( \triangle ABC \) and \( \triangle ARTL \):

Corresponding Angles:

1. \( \angle A \cong \angle A \)
2. \( \angle B \cong \angle R \)
3. \( \angle C \cong \angle T \)

Corresponding Sides: 4. \( AB \cong AR \) 5. \( BC \cong RT \) 6. \( CA \cong TL \)

In summary, the 6 corresponding congruent statements can be listed as:

1. \( \angle A \cong \angle A \)
2. \( \angle B \cong \angle R \)
3. \( \angle C \cong \angle T \)
4. \( AB \cong AR \)
5. \( BC \cong RT \)
6. \( CA \cong TL \)

If you're looking for further simplification or clarification, please let me know!