Question

v is the midpoint of tu. complete the proof that asuv = astv.
1 v is the midpoint of tu given
2 sv 1 tu given
3 ∠svt ≅ ∠svu
4 tv ≅ uv
5 sv ≅ sv reflexive property of congruence
6 △suv ≅ △stv sas

Explanation:

Step1: Determine the reason for ∠SVT ≅ ∠SVU

Since \( \overline{SV}\perp\overline{TU}\), by the definition of perpendicular lines, \( \angle SVT = 90^{\circ}\) and \( \angle SVU=90^{\circ}\). If two angles have the same measure, they are congruent. So the reason is "Definition of perpendicular lines (all right angles are congruent)".

Step2: Determine the reason for \( \overline{TV}\cong\overline{UV}\)

Since \( V\) is the mid - point of \( \overline{TU}\), by the definition of a mid - point, a mid - point divides a segment into two congruent segments. So the reason is "Definition of mid - point".

Answer:

1. Definition of perpendicular lines (all right angles are congruent)
2. Definition of mid - point