Question

reasoning
proofs involving angle congruence
prove: ( m angle 2 = m angle 3 )
3 ( m angle b e d = m angle 1 + m angle 3 )
4 ( m angle a b c = m angle 1 + m angle 2 )
5
validate this line is incorrect.

Explanation:

Step1: Use the given equal angles

Assume \(m\angle AEC=m\angle BED\) (if not given, this is a missing key step).

Step2: Substitute the angle - addition expressions

Since \(m\angle AEC = m\angle1 + m\angle2\) and \(m\angle BED=m\angle1 + m\angle3\), substitute into \(m\angle AEC=m\angle BED\). We get \(m\angle1 + m\angle2=m\angle1 + m\angle3\).

Step3: Subtract \(m\angle1\) from both sides

By the subtraction property of equality, \((m\angle1 + m\angle2)-m\angle1=(m\angle1 + m\angle3)-m\angle1\). Simplifying gives \(m\angle2 = m\angle3\).

Answer:

The correct statement for step 5 should be \(m\angle AEC=m\angle BED\) (from the property of congruent angles, if \(\angle AEC\cong\angle BED\)) and then \(m\angle1 + m\angle2=m\angle1 + m\angle3\) (substitution using angle - addition property from steps 3 and 4), and finally \(m\angle2 = m\angle3\) (subtraction property of equality: subtract \(m\angle1\) from both sides of \(m\angle1 + m\angle2=m\angle1 + m\angle3\)).