Final answer:
The true statement about the triangles on the graph is that the slopes of the two triangles are the same.
Step-by-step explanation:
In the given statement, there are two main points to consider - the sizes of the triangles and their slopes. Firstly, it is stated that the triangles are congruent, which means they are exactly equal in size and shape. This implies that all corresponding sides and angles of the two triangles are equal. Therefore, we can conclude that the slopes of the two triangles must also be equal.
To further understand this, let's define what slope is. In mathematics, slope is a measure of the steepness of a line. It is calculated by dividing the change in the y-coordinate (vertical change) by the change in the x-coordinate (horizontal change) between two points on the line. In this case, the points being referred to are the vertices of the triangles.
Now, let's look at the given statement that the slope of the smaller triangle is smaller than the slope of the larger triangle. This statement is not true because if the two triangles are congruent, then the change in y-coordinate and the change in x-coordinate between corresponding points must be equal. This results in the same slope for both triangles.
Similarly, the statement that the slope of the larger triangle is larger than the slope of the smaller triangle is also not true. As mentioned earlier, the congruency of the triangles implies that all corresponding sides and angles are equal, leading to the same slope for both triangles.
Therefore, it can be concluded that the slopes of the two triangles are the same. This is a direct result of the congruency of the triangles, as all corresponding points have the same change in y-coordinate and change in x-coordinate, resulting in the same slope.
In conclusion, the true statement about the triangles on the graph is that the slopes of the two triangles are the same. This is because the triangles are congruent, resulting in equal corresponding points and thus, equal slopes.