Question

consider △abc and △dcb in the figure below. use the figure above to complete the following. (a) △abc and △dcb have been separated. fill in the missing vertex labels. (b) choose the correct statement below about △abc and △dcb. then fill in the additional information as necessary. the triangles have a common side. common side: (choose one) the triangles have a common angle. common angle: (choose one) the triangles have neither a common side nor a common angle.

Explanation:

Step1: Identify vertices for separated triangles

In \(\triangle ABC\), the vertices are \(A\), \(B\), \(C\). In \(\triangle DCB\), the vertices are \(D\), \(C\), \(B\). For the first separated - triangle with side lengths \(5\) and \(1\), the vertices from left - top to bottom - right are \(A\), \(B\), \(C\). For the second separated - triangle with side lengths \(7\) and \(3\), the vertices from left - top to bottom - right are \(D\), \(C\), \(B\).

Step2: Check for common side or angle

In \(\triangle ABC\) and \(\triangle DCB\), the common side is \(BC\).

Answer:

(a) Left - triangle vertices (from top - left to bottom - right): \(A\), \(B\), \(C\); Right - triangle vertices (from top - left to bottom - right): \(D\), \(C\), \(B\)
(b) The triangles have a common side. Common side: \(BC\)