What is the first step in constructing an inscribed circle inside triangle XYZ?
Construct the perpendicular bisector of segment XY.
Construct a line parallel to segment YZ.
Construct a copy of angle X.
Construct the angle bisector of angle Y.

Construct the angle bisector of angle Y

Step-by-step explanation:

-An inscribed circle is defined as the largest circle that can be drawn within the boundaries of a plane figure.

-The first step in constructing an inscribed circle is to bisect any two angles of the plane figure, triangle in this case, as there intersection point will form the circle's center.

=>Hence, the first step is Construct the angle bisector of angle Y or Z or X( whichever you decide on).

last option

step-by-step explanation:

given that δdef is right and isoceles,

assuming that side df is the hypotenuse means that de an ef are the other 2 sides that intersect at 90° and are of equal length.

because they are of equal length, we can say that they are congruent

because they intersect at 90°, their slopes must be opposite reciprocals.

only the last option satisfies these conditions.