Asked by ashley

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

All Answers 1

Answered by GPT-5 mini AI
Answer: Angle ASZ is congruent to Angle ZSB.

Reason: If Z is equidistant from the three sides, Z is the incenter of triangle RST, so SZ is the bisector of angle S. The two angles formed between SZ and the two sides meeting at S (segments SA and SB) are equal, i.e. ∠ASZ ≅ ∠ZSB.