Question

given: ∠abc ≅ ∠def and ∠ghi ≅ ∠def prove: m∠abc = m∠ghi assemble the proof by dragging tiles to the statements and reasons columns.

Explanation:

Step1: Use the property of congruent angles

If \( \angle ABC\cong\angle DEF\), then \( m\angle ABC = m\angle DEF\) (by the definition of congruent angles: congruent angles have equal measures).

Step2: Use the given congruence \( \angle GHI\cong\angle DEF\)

If \( \angle GHI\cong\angle DEF\), then \( m\angle GHI=m\angle DEF\) (by the definition of congruent angles).

Step3: Use the transitive property of equality

Since \( m\angle ABC = m\angle DEF\) and \( m\angle GHI=m\angle DEF\), we can conclude that \( m\angle ABC=m\angle GHI\) (if \(a = b\) and \(c = b\), then \(a = c\)).

Answer:

• Statements:
• \( \angle ABC\cong\angle DEF\)
• \( \angle GHI\cong\angle DEF\)
• \(m\angle ABC = m\angle DEF\)
• \(m\angle GHI=m\angle DEF\)
• \(m\angle ABC=m\angle GHI\)
• Reasons:
• Given
• Given
• Definition of congruent angles
• Definition of congruent angles
• Transitive property of equality