Question

name _ date _ per _ two column proofs wk directions. fill in the proof tables. 1. given: m∠1 = m∠3 prove: m∠nal = m∠gae statements reasons 1. m∠1 = m∠3 1. 2. 2. addition property of equality 3. m∠1 + m∠2 = m∠__ 3. angle addition postulate 4. m∠ + m∠ = m∠__ 4. 5. m∠nal = m∠gae 5. 2. given: ∠1 is a complement of ∠3 ∠1 = ∠2 prove: ∠2 is a complement of ∠3

Explanation:

Step1: Given information

Given that \(m\angle1 = m\angle3\)

Step2: Apply addition property of equality

Add \(m\angle2\) to both sides: \(m\angle1 + m\angle2=m\angle3 + m\angle2\)

Step3: Use angle - addition postulate

\(m\angle1 + m\angle2=m\angle NAL\) (by angle - addition postulate, as \(\angle1\) and \(\angle2\) form \(\angle NAL\))

Step4: Use angle - addition postulate again

\(m\angle3 + m\angle2=m\angle GAE\) (by angle - addition postulate, as \(\angle3\) and \(\angle2\) form \(\angle GAE\))

Step5: Substitute and conclude

Since \(m\angle1 + m\angle2=m\angle3 + m\angle2\), \(m\angle NAL = m\angle GAE\)

Answer:

Statements	Reasons
2. \(m\angle1 + m\angle2=m\angle3 + m\angle2\)	2. Addition Property of Equality
3. \(m\angle1 + m\angle2=m\angle NAL\)	3. Angle Addition Postulate
4. \(m\angle3 + m\angle2=m\angle GAE\)	4. Angle Addition Postulate
5. \(m\angle NAL = m\angle GAE\)	5. Substitution Property of Equality