Triangle qrs has been translated to create triangle q'r's'. rs= r's' = 10 units, qs= q's' = 5 units, and angles q and q' are both 90 degrees. which theorem below would prove the two triangles are congruent?
a. sss
b. sas
c. asa
d. hl

D. HL

Step-by-step explanation:

Given: Triangle QRS has been translated to create triangle Q'R'S'

such that  RS= R'S' = 10 units,

QS= Q'S' = 5 units,

∠Q =∠ Q'= 90°

∴ Both the triangles are right triangles.

Now, the side opposite to ∠Q in Triangle QRS = RS

and the side opposite to ∠Q'in Triangle Q'R'S' = R'S'

Also, the side opposite to the right angle is the hypotenuse of the triangle.

∴ In ΔQRS and ΔQ'R'S'

RS= R'S' = 10 units [Hypotenuse]

QS= Q'S' = 5 units [Leg]

∠Q =∠ Q'= 90°  [right angle]

∴ By HL theorem,

ΔQRS ≅ ΔQ'R'S'

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d

step-by-step explanation:

step-by-step explanation: