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Given: BC || AD and AB || CD.

Prove: BZD.
Note: quadrilateral properties are not permitted in this proof.
Step
try
Statement
BC AD
AB | CD
AC CA
Type of Statement
A
TE
B
Reason
Given
reflexive Property

Given: BC || AD and AB || CD. Prove: BZD. Note: quadrilateral properties are not permitted-example-1

1 Answer

2 votes

The two column proof has shown that ∠B ≅ ∠D by CPCTC

How to solve two column proof?

The two column proof to show that ∠B ≅ ∠D is as follows:

Statement 1: BC ║ AD

Reason 1: Given

Statement 2: AB ║ CD

Reason 2: Given

Statement 3: AC ≅ CA

Reason 3: Reflexive Property

Statement 4: ∠BCA ≅ ∠DAC

Reason 4: Alternate angles

Statement 5: ∠DCA ≅ ∠BAC

Reason 5: Alternate angles

Statement 6: ΔDCA ≅ ΔBAC

Reason 6: ASA Congruence postulate

Statement 7: ∠B ≅ ∠D

Reason 7: CPCTC

User Juan Jardim
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