Question

AD BC and BCD ADC

Prove:
DE = CE
Angles, Segments, Triangles:
Reasons:
AAS (Angle-Angle-Side)
SAS (Side-Angle-Side)
CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
Given
Statements:
✓ 1. AD BC
✓ 2. ∠DEA and ∠CEB are vertical angles
DC DC
✓ 4. ∠DEA ≅ ∠CEB
Reasons:
Given
Definition of vertical angles
Reflexive property
Vertical angles theorem

Answer 1

To prove that DE = CE, we can use the concept of congruent triangles. By showing that ∆ADE ≅ ∆CEB, we can then conclude that DE = CE.

Step-by-step explanation:

To prove DE = CE, we can use the concept of congruent triangles. Given that AD = BC (given statement 1) and ∠DEA ≅ ∠CEB (given statement 4), we can apply the AAS (Angle-Angle-Side) congruence criterion. By showing that ∆ADE ≅ ∆CEB, we can then conclude that DE = CE.

Step 1: ∠DEA ≅ ∠CEB (given statement 4)

Step 2: AD = BC (given statement 1)

Step 3: ∆ADE ≅ ∆CEB (AAS criterion using steps 1 and 2)

Step 4: DE = CE (corresponding parts of congruent triangles are congruent, CPCTC)