Question

Point Z is equidistant from the sides of ΔRST. Point Z is equidistant from the sides of triangle R S T. Lines are drawn from the point of the triangle to point Z. Lines are drawn from point Z to the sides of the triangle to form right angles and line segments Z A, Z B, and Z C. Which must be true? Line segment S Z is-congruent-to line segment T Z Line segment R Z is-congruent-to line segment B Z AngleCTZ Is-congruent-to AngleASZ AngleASZ Is-congruent-to AngleZSB

Answer 1

AngleASZ Is-congruent-to AngleZSB

Explanation:

D is the correct answer

Answer 2

AngleASZ Is-congruent-to AngleZSB

Explanation:

The incenter of a triangle is a point inside a triangle that is equidistant from all the sides of a triangle. The incenter is the point formed by the intersection of all the three angles of the triangle bisected. The lines drawn from the incenter to the sides of the triangle forming right angles to the sides are congruent.

If Point Z is equidistant from the sides of ΔRST, point Z is the incenter of triangle RST. Lines are drawn from point Z to the sides of the triangle to form right angles and line segments Z A, Z B, and Z C. This lines are therefore congruent to each other, i.e. ZA = ZB = ZC.. Since the angles of the sides of the triangles are bisected to form the incenter, therefore:

AngleASZ Is-congruent-to AngleZSB