Question

drag the tiles to the correct boxes to complete the pairs.
in the figure, lines hj and kl are parallel.
match each angle relationship with the appropriate reason.
same-side interior angles
corresponding angles theorem
alternate exterior angles theorem
linear pair
vertical angles theorem
alternate interior angles theorem
$m\angle kfe = m\angle fej$
$m\angle lfg = m\angle deh$
$m\angle dej = m\angle efl$
$m\angle hed = m\angle fej$
$m\angle jef + m\angle lfe = 180^\circ$
$m\angle efg + m\angle gfk = 180^\circ$

Explanation:

1. For $m\angle KFE = m\angle FEJ$: These angles lie between parallel lines HJ and KL, on opposite sides of transversal EF, so they are alternate interior angles.
2. For $m\angle LFG = m\angle DEH$: These angles lie outside parallel lines HJ and KL, on opposite sides of transversal DG, so they are alternate exterior angles.
3. For $m\angle DEJ = m\angle EFL$: These angles occupy matching positions relative to the parallel lines and transversal EF, so they are corresponding angles.
4. For $m\angle HED = m\angle FEJ$: These angles are opposite each other where lines HD and FJ intersect, so they are vertical angles.
5. For $m\angle JEF + m\angle LFE = 180^\circ$: These angles lie between parallel lines HJ and KL, on the same side of transversal EF, so they are same-side interior angles.
6. For $m\angle EFG + m\angle GFK = 180^\circ$: These angles form a straight line, so they are a linear pair.

Answer:

$m\angle KFE = m\angle FEJ$ $
ightarrow$ Alternate interior angles theorem
$m\angle LFG = m\angle DEH$ $
ightarrow$ Alternate exterior angles theorem
$m\angle DEJ = m\angle EFL$ $
ightarrow$ Corresponding angles theorem
$m\angle HED = m\angle FEJ$ $
ightarrow$ Vertical angles theorem
$m\angle JEF + m\angle LFE = 180^\circ$ $
ightarrow$ same-side interior angles
$m\angle EFG + m\angle GFK = 180^\circ$ $
ightarrow$ linear pair