Question

given: $overline{de}paralleloverline{gf},overline{ef}paralleloverline{dg}$
prove: $mangle edg = mangle efg$

1. $mangle1 = mangle4$, $mangle2 = mangle3$
2. if two parallel lines are cut by a trans - versal, then their alternate interior angles are equal.
3. $mangle1 + mangle2 = mangle4 + mangle3$
4. addition property
5. $mangle edg = mangle1 + mangle2$ and $mangle efg = mangle3 + mangle4$
6. click here to insert
7. click here to insert
8. substitution property

Explanation:

Step1: Identify postulate for step 4

By the Angle - Addition Postulate, an angle is the sum of its non - overlapping adjacent angles. So, $m\angle EDG = m\angle1 + m\angle2$ and $m\angle EFG=m\angle3 + m\angle4$.

Step2: Use substitution for step 5

Since $m\angle1 + m\angle2=m\angle4 + m\angle3$ (from step 3) and $m\angle EDG = m\angle1 + m\angle2$, $m\angle EFG=m\angle3 + m\angle4$, by the Substitution Property, we can substitute to get $m\angle EDG=m\angle EFG$.

Answer:

1. Angle - Addition Postulate
2. $m\angle EDG=m\angle EFG$