To determine which statement is true based on the given options, we would need to look at the properties of the segments and angles in the provided figure. However, since I cannot see the picture, I can't directly evaluate which statement is true.
Here’s how you might assess each statement:
- CD = AD: This could indicate that D is the midpoint of AC, but without seeing the figure, we cannot confirm.
- AC = CB: This could suggest that point C is the midpoint of AB.
- BD = BC: This statement could relate to an angle being bisected or it indicates an isosceles triangle depending on the positions of the points.
- AD = CB: This might be true if there is symmetry or some midpoint scenario, but again, it depends on the figure.
Next, let’s analyze the theorems:
- Perpendicular Bisector Theorem: This states that any point on a perpendicular bisector of a segment is equidistant from the endpoints of that segment.
- Vertical Angle Theorem: This states that vertical angles are always equal.
- Alternate Interior Angle Theorem: This states that if two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
- Triangle Inequality Theorem: This essentially states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
Without the specific picture or any context, it would be difficult to definitively pick a true statement or a theorem that proves it. You will need to analyze the figure according to the relationships among the points and apply the appropriate geometry concepts or theorems.
If you can describe the figure or its properties, I’d be happy to help more specifically!