Question

question 3 of 5
select the correct answer.
which triangle is congruent to triangle abc?
○ triangle jkl
○ triangle def
○ triangle ghi
○ triangle mno

Explanation:

Step1: Identify ABC's side lengths

First, find coordinates of A(1,2), B(1,4), C(4,4).
Vertical side AB: $|4-2|=2$
Horizontal side BC: $|4-1|=3$
Hypotenuse AC: $\sqrt{(4-1)^2+(4-2)^2}=\sqrt{9+4}=\sqrt{13}$

Step2: Check triangle GHI's sides

Coordinates: G(-2,-2), H(-2,-4), I(-5,-4)
Vertical side GH: $|-4-(-2)|=2$
Horizontal side HI: $|-5-(-2)|=3$
Hypotenuse GI: $\sqrt{(-5+2)^2+(-4+2)^2}=\sqrt{9+4}=\sqrt{13}$

Step3: Verify congruence

All corresponding sides of △ABC and △GHI are equal, so they are congruent by SSS.

Answer:

triangle GHI