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Given the picture, which of the following statements is true? (Picture is not drawn to scale)

(1 point)
Responses

CD = AD
CD = AD

AD = CB
AD = CB

BD = BC
BD = BC

AC = CB
AC = CB
Question 2
Which theorem proves this?(1 point)
Responses

Triangle Inequality Theorem
Triangle Inequality Theorem

Alternate Interior Angle Theorem
Alternate Interior Angle Theorem

Vertical Angle Theorem
Vertical Angle Theorem

Perpendicular Bisector Theorem

1 answer

I'm unable to see the picture. However, I can help guide you based on standard geometric principles if you can provide more information about the relationships between the segments or angles in question.

For Question 1 about which statements could be true, here are some considerations:

  1. CD = AD: This statement suggests that two segments are of equal length. This can be true in certain cases, such as if CD is the segment being bisected at point D.

  2. AD = CB: This indicates that two segments could be equal under specific geometric properties such as symmetry or congruence of triangles.

  3. BD = BC: This could be true if B represents a midpoint or if some property of the triangle being considered allows for this equality to hold.

  4. AC = CB: Again, this could be true in some circumstances, such as if triangle ABC is isosceles.

You would need to assess these relationships based on the properties and definitions given in your specific diagram.

For Question 2 concerning which theorem proves the statement made in Question 1, here's a brief outline of each option:

  1. Triangle Inequality Theorem: This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. It may apply if comparing lengths of segments that are sides of a triangle.

  2. Alternate Interior Angle Theorem: This theorem states that if two parallel lines are cut by a transversal, the pairs of alternate interior angles are equal. This theorem is not directly related to segment lengths.

  3. Vertical Angle Theorem: This states that opposite angles formed by two intersecting lines are equal. While it can prove angle relationships, it doesn’t directly influence segment lengths.

  4. Perpendicular Bisector Theorem: This theorem indicates that any point on the perpendicular bisector of a segment is equidistant from the endpoints of that segment. It could be useful if determining distances from a bisector.

If you can provide more context regarding the relationships of the segments, I can help you identify the correct answers.