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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?
Line segment T A is-congruent-to line segment T B
Line segment A Z is-congruent-to line segment B Z
AngleBTZ Is-congruent-to AngleBUZ
AngleTZA Is-congruent-to AngleTZB

Answer :

An isosceles triangle is one with two equal-length sides. The correct option is C.

What is an isosceles triangle?

An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.

The diagram as per the given conditions is drawn below.

In ΔUTZ, since the sides UZ and TZ are equal because the point z is equidistance from T and U, therefore, the triangle is an isosceles triangle. Thus, ∠BTZ≅TZB.

Hence, the correct option is C.

Learn more about Isosceles Triangle:

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