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.
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.
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