Questions: Given: ∠ABC ≅ ∠DEF and ∠GHI ≅ ∠DEF Prove: m∠ABC = m∠GHI Enter Reasons m∠GHI = ∠ABC ∠DEF ∠GHI Statements 1. ∠GHI ≅ ∠DEF 2. ∠ABC ≅ ∠DEF Reasons 1. given 2. given

Solution Steps

To prove that the measures of angles ∠ABC and ∠GHI are equal, we can use the transitive property of congruence. Since ∠ABC is congruent to ∠DEF and ∠GHI is also congruent to ∠DEF, it follows that ∠ABC is congruent to ∠GHI. Therefore, the measures of ∠ABC and ∠GHI are equal.

We are given that \(\angle ABC \cong \angle DEF\) and \(\angle GHI \cong \angle DEF\). This means that the measures of these angles are equal: \(m\angle ABC = m\angle DEF\) and \(m\angle GHI = m\angle DEF\).

The transitive property of congruence states that if two angles are each congruent to a third angle, then they are congruent to each other. Therefore, since \(\angle ABC \cong \angle DEF\) and \(\angle GHI \cong \angle DEF\), it follows that \(\angle ABC \cong \angle GHI\).

Since \(\angle ABC \cong \angle GHI\), the measures of these angles are equal. Thus, we have: \[ m\angle ABC = m\angle GHI \]

Final Answer