Chapter 10.1, Problem 2CE

To determine

To Find: The type of triangle is $\Delta XYZ$ .

Answer to Problem 2CE

The triangle is equilateral and is shown in Figure 1

Explanation of Solution

Given:

Construct $\overline{XY}$ so that $XY=AB$ .

Use X and Y as the centre and the radius equal to AB draw arcs that intersect. Label the point of intersection Z.

Draw $\overline{XZ}$ and $\overline{YZ}$

What kind of triangle is $\Delta XYZ$ .

Calculation:

Consider the line $AB$ and draw the line $\overline{XY}$ such that $XY=AB$ .

Consider the X and Y as centre and equal radius to draw an arc. Consider the intersection point that is named Z and draw $\overline{XZ}$ and $\overline{YZ}$ such that it form the triangle with all the sides are equal.

In case all the sides are equal then the triangle is equilateral as shown in Figure 1

  

Figure 1