Final answer:
To determine congruency of triangles on a coordinate plane, one must assess whether all corresponding pairs of sides and angles are congruent. Calculations using the Pythagorean Theorem and trigonometric ratios are necessary to verify this. Without more context or the measurements of the illustrated triangle, a definitive answer can't be provided.
Step-by-step explanation:
To determine which triangle defined by three points on the coordinate plane is congruent with the given triangle, one must ascertain that all corresponding pairs of sides and angles are congruent. Congruency in triangles means that one can be transformed into the other through rotation, reflection, or translation, without altering their size or shape. We will compare the given sets of points to see if they form congruent triangles.
Option 1 and 3 provide the same points, (0, -4), (6, 6), and (6, -4), possibly forming a right-angled triangle due to the perpendicular lines formed from the y-axis and parallel to the x-axis. To confirm congruency through sides and angles, we would calculate the distances between the points to get the lengths of the sides and use trigonometry such as the sine, cosine, and tangent ratios or the Pythagorean Theorem to find the angles in the case of a right-angled triangle. Only if both sides and angles are congruent can we ascertain true congruency.
Option 4 mentions the points (0, -2), (3, 3), and (3, -2), similarly suggesting a right-angled triangle. As with the earlier option, assessing congruency would require side length comparisons and angle calculations.
The decision between options 1/3 and 4 should be based on the actual measurements and calculations of the sides and angles. Without knowing which triangle is illustrated as the standard for comparison, we cannot conclusively state which option is correct. Therefore, an exact answer cannot be given without those calculations or additional information.