Question

In the figure to the right, can you conclude that triangle GHI is congruent to triangle KJI? Justify your reasoning.

Answer 1

No

Explanation:

You cannot conclude that ΔGHI is congruent to ΔKJI, because although you can see/interpret that there all the angles are congruent with one another, like with vertical angles (∠GIH and ∠KIJ) and alternate interior angles (∠H and ∠J, ∠G and ∠K), we don't know the side lengths.

All the angles could be congruent, but the sides might be different. For example, ΔGHI might be a bigger triangle than ΔKJI, which could make them similar to one another, but not congruent.

For something to be congruent to another, everything must be exactly the same.