Given: l || m; ∠1 ∠3 Prove: p || q Complete the missing parts of the paragraph proof. We know that angle 1 is congruent to angle 3 and that line l is parallel to line m because . We see that is congruent to by the alternate interior angles theorem. Therefore, angle 1 is congruent to angle 2 by the transitive property. So, we can conclude that lines p and q are parallel by the

p║q hence proved.

Step-by-step explanation:

In the question given parameters are line l║m and ∠1 = ∠3

and we have to prove p║q.

Since ∠1 = ∠3 (given)

Opposite angle of ∠1 = ∠2 (Alternate interior angles)

Therefore ∠2 = ∠3 (Transitive property)

∠2 = ∠3 are congruent when lines p and q are parallel and lines l and m are transverse.

Therefore p║q.

Hence proved.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240