Which triangle must be a right triangle and why?

Option 4 is correct: ΔBGC is right angle because line EG ⊥ line segment CC'.

Step-by-step explanation:

Right Angled triangle is triangle with measure of one angle 90°.

Option A:

ΔA'B'C' is not right traingle because no angle if of 90° and image has no role in it. It only work if ΔABC is also a right angle traingle but it is not.

Option B:

Intersection of line/line segment has no role in right triangle if it does not intersect at right angle. ∴ ΔADC is not right angled triangle.

Option C:

ΔBCC' is not right angled triangle because thee is not right angle and point B lies on line of reflection has no role in it.

Option D:

ΔBGC is right angle triangle because m∠BGC = 90°.

m∠BGC = 90° as line EG is perpendicular to CC' at G.

Option D is correct.

answer: -2+√x,-2-√x

i hope this , i don't know if you're looking for a pair or not.