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'

The total area:

12 units²

Step-by-step explanation:

There are three parts on this shape:

1 big right triangle

1 rectangle

1 small right triangle

area = (4*4)/2 = 16/2 = 8units²

area = 2*1 = 2units²

area = (2*2)/2 = 2units²

8+2+2 = 12 units²