Chapter 12.4, Problem 16Q

(a)

To determine

To Classify: The triangle $1-4$ by their angles.

Answer to Problem 16Q

  $\begin{array}{l}\Delta 1=Righttriangle\\ \Delta 2=Obtusetriangle\\ \Delta 3=Acutetriangle\\ \Delta 4=Equilateraltriangle\end{array}$

Explanation of Solution

Given:

  

  $\begin{array}{l}\Delta 1=Righttriangle\\ \Delta 2=Obtusetriangle\\ \Delta 3=Acutetriangle\\ \Delta 4=Equilateraltriangle\end{array}$

(b)

To determine

To Classify: The triangle $4-6$ by their sides.

Answer to Problem 16Q

  $\begin{array}{l}\Delta 4=Equilateraltriangle\\ \Delta 5=scalenetriangle\\ \Delta 6=Isoscelestriangle\end{array}$

Explanation of Solution

Given:

  

  $\begin{array}{l}\Delta 4=Equilateraltriangle\\ \Delta 5=scalenetriangle\\ \Delta 6=Isoscelestriangle\end{array}$

(c)

To determine

To Find: Is there enough information given to prove $\Delta 7\cong \Delta 8$ . If so label the vertices and write a proof and if not determine what additional information is required.

Answer to Problem 16Q

The given information is enough.

Explanation of Solution

Given:

  

  

In

  $\begin{array}{l}\Delta ABCand\Delta DEF\\ AB\cong DE\\ AC\cong DF\\ \angle BAC\cong \angle EDF\\ thus\\ bySAS\\ \Delta ABC\cong \Delta DEF\end{array}$

The given information is enough.