<2=<4, m<2= 110 degrees Given m∠2 = m∠4 Definition of congruent angles m∠4 = 110º
Complete the 2 column proof
To complete the two-column proof, we will need to list the statements on the left column and the corresponding reasons on the right column.
Here is the completed two-column proof:
Statement Reason
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1. <2 = <4 Given
2. m<2 = 110º Given
3. m<2 = m<4 Definition of congruent angles
4. m<4 = 110º Substitution (using statement 2)
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In the proof, Statement 1 is the given condition that <2 is congruent to <4. Statement 2 is another given piece of information, stating that the measure of <2 is 110 degrees.
To reach Statement 3, we use the definition of congruent angles, which states that if two angles are congruent, then their measures are equal. Since <2 is congruent to <4 (statement 1), we can conclude that m<2 (the measure of <2) is equal to m<4 (the measure of <4).
Finally, in Statement 4, we substitute the measure of <2 (110 degrees) into the equation, as stated in Statement 3. Therefore, we can assert that m<4 is also equal to 110 degrees.
Statement Reason
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1. <2=<4 Given
2. m<2 = 110° Given
3. m∠2 = m∠4 Definition of congruent angles
4. m∠4 = 110° Transitive property of equality
Hence, the two-column proof is complete.