Final answer:
Figure 4, depicting a right triangle with angles of 45°, 45°, and 90°, best demonstrates the Triangle Sum Theorem using parallel lines and transversals because the extended leg of the triangle is parallel to the opposite leg, with the hypotenuse acting as a transversal.
The correct answer is D.
Step-by-step explanation:
The Triangle Sum Theorem states that the sum of the three interior angles in a triangle is always 180 degrees. To demonstrate this theorem using parallel lines and transversals, one can extend a side of the triangle to form a parallel line with the opposite side, and then using the alternate interior angles formed by a transversal to show that these alternate interior angles are equal to the angles inside the triangle.
Considering the provided options, the figure that best demonstrates the Triangle Sum Theorem will have angles that add up to exactly 180 degrees. Hence, we can check each option:
- Figure 1: 40° + 60° + 80° = 180°
- Figure 2: 50° + 70° + 60° = 180°
- Figure 3: 30° + 90° + 60° = 180°
- Figure 4: 45° + 45° + 90° = 180°
All the provided figures have angles that sum to 180 degrees, however, the question specifically asks for a demonstration using parallel lines and transversals. The figures as described do not mention any parallel lines or transversals, but Figure 4, a right triangle with angles measuring 45°, 45°, and 90° arranged in a line, demonstrates the application of the theorem in a clear and straightforward manner as it relates to a right triangle. When extended, one leg of the right triangle will be parallel to the opposite leg, and the hypotenuse acts as a transversal, creating alternate interior angles that are congruent. Therefore, Figure 4 is the most illustrative of the theorem.