Point Z is equidistant from the vertices of ΔTUV.Point Z is equidistant from the vertices of triangle T U V. 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?A.Line segment T A is-congruent-to line segment T BB.Line segment A Z is-congruent-to line segment B ZC.AngleBTZ Is-congruent-to AngleBUZD.AngleTZA Is-congruent-to AngleTZB
Accepted Solution
A:
Answer:option C. Angle BTZ Is-congruent-to Angle BUZStep-by-step explanation:Point Z is equidistant from the vertices of triangle T U VSo, ZT = ZU = ZVWhen ZT = ZU ∴ ΔZTU is an isosceles triangle ⇒ ∠TUZ=∠UTZ When ZT = ZV ∴ ΔZTV is an isosceles triangle ⇒ ∠ZTV=∠ZVTWhen ZU = ZV ∴ ΔZUV is an isosceles triangle ⇒ ∠ZUV=∠ZVUFrom the figure ∠BTZ is the same as ∠UTZAnd ∠BUZ is the same as ∠TUZ So, the statement that must be true is option CC.Angle BTZ Is-congruent-to Angle BUZ