(02.03 mc)

triangle abc with a at 0 comma 0, b at 2 comma 4 and c at 0 comma 2, the measure of angle c is 135 degrees, and the measure of angle a is 45 degrees, triangle def with d at 2 comma 0, e at 4 comma 4 and f at 4 comma 2, the measure of angle f is 135 degrees, and the measure of angle e is 45 degrees

name the congruent triangles and justify the reason for congruence.

δabc ≅ δfde by hl
δabc ≅ δedf by asa
δabc ≅ δfed by hl
δabc ≅ δfed by asa

answer: get jesus in your life

step-by-step explanation:

(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