Question

which of these statements is true about the two triangles graphed below? a. they are congruent, because one can be obtained by reflecting the other across the x - axis. b. they are congruent, because one can be obtained by reflecting the other across the y - axis.

Explanation:

To determine the truth about the two triangles, we analyze the reflection. Reflecting a figure across the x - axis changes the sign of the y - coordinates of its vertices. Let's check the vertices:

• For the upper triangle, a vertex like (2, 2) (assuming the lower triangle's corresponding vertex is (2, - 2)): reflecting (2, 8) across the x - axis gives (2, - 8), (2, 2) across x - axis gives (2, - 2), and (12, 8) across x - axis gives (12, - 8), which matches the lower triangle's vertices. Reflecting across the y - axis would change the sign of x - coordinates, but the x - coordinates of the triangles are the same (both have x from 2 to 12), so reflection across y - axis is not the case. So the triangles are congruent as one is the reflection of the other across the x - axis.

Answer:

A. They are congruent, because one can be obtained by reflecting the other across the x - axis.