Question

Using CPCTC Angles Segments Triangles Statements Reasons Given: AD BC and BCD LADC Prove: DE CE Statements Reasons Assemble the proof by dragging tiles to the Statements and Reasons columns.​

Answer 1

The question is about using CPCTC to prove that DE is congruent to CE. By constructing two triangles and using the given information, we can show that the corresponding angles are congruent, and thereby conclude that the corresponding sides are congruent as well.

Step-by-step explanation:

The question is related to CPCTC (Corresponding Parts of Congruent Triangles are Congruent), which is a proof technique used in geometry to prove that corresponding parts of congruent triangles are congruent. The given information states that AD is congruent to BC and angle BCD is congruent to angle LADC. The objective is to prove that DE is congruent to CE.

To prove this, we can construct two triangles: triangle AED and triangle CEB. Using the given information, we can show that angle EAD is congruent to angle ECB and angle AED is congruent to angle CEB. By the CPCTC theorem, we can then conclude that DE is congruent to CE. Therefore, DE is congruent to CE.