Write a two-column proof.
given: quadrilateral gkjh is a parallelogram
prove: triangle glh is congruent to triangle jlk

A parallelogram has two pairs of opposite parallel congruent sides.

Given :

Quadrilateral GKJH is a parallelogram,

To prove :

Δ GLH ≅ Δ JLK

Proof :

          Statement                                     Reason

1.   GH ║ KJ                                      Definition of parallelogram

2. ∠LGH ≅ ∠LJK, ∠LHK ≅ ∠LKJ     Alternate interior angle theorem

3. GH ≅ KJ                                        Definition of parallelogram

4.  Δ GLH ≅ Δ JLK                            ASA postulate of congruence

Hence, proved...

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

$650 per month plus utilities

step-by-step explanation:

just based on the info you gave, it would seem more cost effective to rent at $650 per month plus utilities.   if utilities are, in fact, $150 per month, your monthly living costs would be $800 as opposed to the other option of $825.