Question

consider \\( \triangle a b c \\) and \\( \triangle d c b \\) in the figure below.

use the figure above to complete the following.

(a) \\( \triangle a b c \\) and \\( \triangle d c b \\) have been separated. fill in the missing vertex labels.

(b) choose the correct statement below about \\( \triangle a b c \\) and \\( \triangle d c b \\).
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:

(a)

Step1: Identify vertices of \(\triangle ABC\)

In \(\triangle ABC\), the vertices are \(A\), \(B\), and \(C\). The side with label \(4\) is \(AB\), the side with label \(1\) is \(BC\). So the vertices (from top - left, bottom - left, bottom - right) are \(A\), \(B\), \(C\)

Step2: Identify vertices of \(\triangle DCB\)

In \(\triangle DCB\), the vertices are \(D\), \(C\), and \(B\). The side with label \(8\) is \(DC\), the side with label \(3\) is \(CB\). So the vertices (from bottom - left, bottom - right, top) are \(B\), \(C\), \(D\)

(b)

Step1: Check for common side

In \(\triangle ABC\) and \(\triangle DCB\), side \(BC\) (or \(CB\)) is common to both triangles.

Answer:

(a) For the first separated triangle (left - hand side): top - vertex \(A\), bottom - left vertex \(B\), bottom - right vertex \(C\); for the second separated triangle (right - hand side): bottom - left vertex \(B\), bottom - right vertex \(C\), top vertex \(D\)

(b) The triangles have a common side. Common side: \(BC\) (or \(CB\))