Question

Draw any $\overline{AB}$.

$\left(a\right).$ Construct $\overline{XY}$ so that $XY=AB$.

$\left(b\right).$ Using $X$ and $Y$ as centers, and a radius equal to $AB,$ draw arcs that intersect. Label the point of intersection $Z$.

$\left(c\right).$ Draw $\overline{XZ}$ and $\overline{YZ}$.

$\left(d\right).$ What kind of triangle is $\Delta XYZ?$

Short answer

The triangle isequilateral.

Step-by-step solution

Step 1. Given information.

Two triangle is given, $\Delta ABC$ and $\Delta XYZ$.

Step 2. Concept used.

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.

Step 3. Draw the figure.

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

Therefore, the triangle isequilateral as shown in the figure.