Question

triangles abd and cbd are shown. if m∠bdc = 70°, what is the relationship between ab and bc? ab = bc ab < bc ab > bc ab + bc < ac

Explanation:

Step1: Analyze the given information

We know that \(AD = DC\) (from the equal - length marks) and \(\angle BDC=70^{\circ}\), so \(\angle BDA = 180^{\circ}-\angle BDC=110^{\circ}\)

Step2: Apply the Side - Angle Relationship in Triangles

In \(\triangle ABD\) and \(\triangle CBD\), \(AD = DC\) and \(BD\) is common. In \(\triangle ABD\), \(\angle BDA = 110^{\circ}\), and in \(\triangle CBD\), \(\angle BDC = 70^{\circ}\). According to the rule that in a triangle, the side opposite the larger angle is longer. Since \(\angle BDA>\angle BDC\), the side opposite \(\angle BDA\) (which is \(AB\)) is longer than the side opposite \(\angle BDC\) (which is \(BC\)). So \(AB > BC\)

Answer:

C. \(AB>BC\)