Question

question 1
daniel is constructing a fence that consists of parallel sides (overline{ab}) and (overline{ef}). complete the proof to explain how he can show that (mangle gkb = 120^{circ}) by filling in the missing justifications.

statement	justification
(mangle elj = 120^{circ})	given
(mangle elj+mangle elk = 180^{circ})	linear - pair postulate
(mangle bkl+mangle gkb = 180^{circ})	linear - pair postulate
(mangle elj + mangle elk=mangle bkl + mangle gkb)	transitive property
(angle elkcongangle bkl)	1
(mangle elk = mangle bkl)	2
(mangle elj + mangle elk=mangle elk + mangle gkb)	substitution property
(mangle elj=mangle gkb)	subtraction property
(mangle gkb=mangle elj)	symmetric property
(mangle gkb = 120^{circ})	substitution

1. alternate interior angles theorem, 2. definition of congruence
2. alternate exterior angles theorem, 2. substitution property
3. definition of congruence, 2. alternate interior angles theorem
4. substitution property, 2. alternate exterior angles theorem

Explanation:

Step1: Identify congruent angles

Since $\overline{AB}\parallel\overline{EF}$, by the Alternate Interior Angles Theorem, $\angle ELK\cong\angle BKL$. The justification for $\angle ELK\cong\angle BKL$ is the Alternate Interior Angles Theorem.

Step2: Use congruence definition

If two angles are congruent, their measures are equal. So the justification for $m\angle ELK = m\angle BKL$ is the Definition of Congruence.

Answer:

1. Alternate Interior Angles Theorem
2. Definition of Congruence