4. given: ∠n ≅ ∠s, line ℓ bisects at q.
prove: ∆nqt ≅ ∆sqr

which reason justifies step 2 in the proof?

if two lines are parallel, then the same-side interior angles formed are congruent.

if two lines are parallel, then the corresponding angles formed are congruent.

vertical angles are congruent.

if two lines are parallel, then the alternate interior angles formed are congruent.

Vertical angles are congruent.

Step-by-step explanation:

In the given picture, NS and RT are intersecting line segments, intersects at point Q.

We know that when two lines intersect to make an cross, angles on opposite sides of the cross are called vertical angles. These angles are equal by the theorem that says Vertical angles are congruent.

⇒∠NQT ≅ ∠SQR

Therefore, the reason that justifies the step 2 :- ∠NQT ≅ ∠SQR is "Vertical angles are congruent" in the proof.

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.