Chapter 14.4, Problem 38WE

a.

To determine

To construct: Equilateral triangle $\Delta ABC$

Answer to Problem 38WE

Equilateral triangle $\Delta ABC$ is plotted.

Explanation of Solution

Given:

Parallel lines $l$ and $k$ with point $A$ .

Concept Used:

A rotation is a transformation suggested by rotating a paddle wheel. When wheel stops, new position of a paddle referred as the image of initial position.

Calculation:

As per the given problem

  

Parallel lines $l$ and $k$ with point $A$ .

To construct equilateral $\Delta ABC$ steps given in question is used.

  

Hence,

Equilateral triangle $\Delta ABC$ is plotted.

b.

To determine

To proof: Triangle $\Delta ABC$ is equilateral.

Answer to Problem 38WE

Explanation of Solution

Given:

Parallel lines $l$ and $k$ with point $A$ .

Concept Used:

A rotation is a transformation suggested by rotating a paddle wheel. When wheel stops, new position of a paddle referred as the image of initial position.

Calculation:

As per the given problem

  

Parallel lines $l$ and $k$ with point $A$ .

  

As we can see all the sides of $\Delta ABC$ are of same length.

Hence,

Triangle $\Delta ABC$ is equilateral.

c.

To determine

To check: Another equilateral triangle.

Answer to Problem 38WE

Explanation of Solution

Given:

Parallel lines $l$ and $k$ with point $A$ .

Concept Used:

A rotation is a transformation suggested by rotating a paddle wheel. When wheel stops, new position of a paddle referred as the image of initial position.

Calculation:

As per the given problem

  

Parallel lines $l$ and $k$ with point $A$ .

  

As we can see $\Delta ABC$ , there will be no other preimage point on line $l$ of point $B$ .

Hence,

No another equilateral triangle.