Question

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 B
B.Line segment A Z is-congruent-to line segment B Z
C.AngleBTZ Is-congruent-to AngleBUZ
D.AngleTZA Is-congruent-to AngleTZB

Answer 1

option C. Angle BTZ Is-congruent-to Angle BUZ

Explanation:

Answer 2

option C. Angle BTZ Is-congruent-to Angle BUZ

Explanation:

Point Z is equidistant from the vertices of triangle T U V

So, ZT = ZU = ZV

When ZT = ZU ∴ ΔZTU is an isosceles triangle ⇒ ∠TUZ=∠UTZ

When ZT = ZV ∴ ΔZTV is an isosceles triangle ⇒ ∠ZTV=∠ZVT

When ZU = ZV ∴ ΔZUV is an isosceles triangle ⇒ ∠ZUV=∠ZVU

From the figure ∠BTZ is the same as ∠UTZ

And ∠BUZ is the same as ∠TUZ

So, the statement that must be true is option C

C.Angle BTZ Is-congruent-to Angle BUZ