(a) State the Hinge Theorem.(b) Let \( A, B, C, \) and \( D \) be four coplanar points such that no three of \( A, B, C, \) and \( D \) are collinear, \( \overline{AD} \cong \overline{BD} \cong \overline{CD} \), and \( B \) is in the interior of \( \angle ADC \). Show that \( AB < AC < AB + BC \).

Hinge Theorem: If two sides of one triangle are congruent to the two sides of another triangle and the included angle of the second triangle is smaller than the included angle of the first triangle, then the third side of the second triangle will be smaller than the third side of the first triangle. As per the given situations:1. DA≅DB≅DC2. B is in the interior of the ∠CAD. From the above figure it is clear that,In △ADC and △ADB1. DB≅DC (condition 1)2. AD common 3. ∠CDA > ∠BDA (using given condition 2)Hence, as per the Hinge's theoremAB < AC. (1)Triangle inequality Theorem: In any triangle, sum of any two sides of the given triangle is always greater than its third side.In △ABCAB + BC > AC (triangle inequality theorem) (2)Combining (1) and (2)AB<AC< AB+BC