Question

given: ( mangle aec = mangle bed )
prove: ( mangle 2 = mangle 3 )
step statement reason
1 ( mangle aec = mangle bed ) given
2 (square) multiplication and division properties
validate this line is incorrect.

Explanation:

Step1: Analyze the given angles

We know that \(m\angle AEC=m\angle2 + m\angle1\) and \(m\angle BED=m\angle3 + m\angle1\) (Angle - addition postulate).

Step2: Use the given equality

Since \(m\angle AEC = m\angle BED\) (given), substitute the angle - addition expressions: \(m\angle2 + m\angle1=m\angle3 + m\angle1\).

Step3: Apply the subtraction property of equality

Subtract \(m\angle1\) from both sides of the equation \(m\angle2 + m\angle1=m\angle3 + m\angle1\). We get \(m\angle2=m\angle3\) (Subtraction property of equality: if \(a + c=b + c\), then \(a = b\)).

Answer:

The reason for step 2 should be the Subtraction Property of Equality (not Multiplication and Division Properties). The correct statement for step 2 is \(m\angle AEC−m\angle1=m\angle BED - m\angle1\) (based on the Subtraction Property of Equality, which states that if \(a = b\), then \(a - c=b - c\)).