What is the property you can use to prove that both △RST and △RUT are congruent?

ASA property

Explanation

We will show that two angles and the side between them in one triangle are congruent, respectively, to two angles and the side between them in a second triangle.  Then we know that the two triangles are congruent by the ASA property.

From the measure of the angles on the figure, we know that two pairs of angles are congruent.

∠SRT ≅ ∠URT and ∠STR ≅ ∠UTR

From the figure, we see that the triangles have side \( \overline{RT} \) in common.  Furthermore, \( \overline{RT} \) is between each pair of congruent angles listed above.  Since every segment is congruent to itself, we also have \( \overline{RT} \cong \overline{RT} \).

Knowing that two angles and the side between them in △RST are congruent, respectively, to two angles and the side between them in △RUT, we can conclude that △RST ≅ △RUT by the ASA property.