A student is investigating pairs of triangles that have congruent corresponding angles. The student claims that for such a pair of triangles, a sequence of rigid motions carries one triangle to the other since the triangles are congruent. Which statement best describes the student's claim? A.) The claim is never true for any such pairs of triangles, since the triangles are similar but not congruent.

B.) The claim is only true if the triangles are equilateral triangles, since the triangles will be of equal shapes and size.

C.) The claim is always true for all such pairs of triangles, since congruent triangles have corresponding angles that are congruent.

D.) The claim is always true of the triangles have congruent sides, since the definition of congruence requires angles and sides.

the correct answer to your question is a. 4^4

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(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

yes, i think so although i am not sure. this is a very strange question.