Question

3 multiple choice 25 points state how the triangles are congruent. indique cómo los triángulos son congruentes. image of triangle with vertices t, u, w, v; segments tu and vw have tick marks; angles at u and w are marked options: hl, aas or saa, ass or ssa, sas, asa, aaa, sss

Explanation:

To determine triangle congruence, we analyze the given diagram. The triangles share the side \( UW \) (common side). We have two sides marked as equal ( \( TU = WV \) from the tick marks) and the included angles \( \angle TUW \) and \( \angle WVU \) (wait, actually, looking at the angles at \( U \) and \( W \), the included angle between the equal sides and the common side. Wait, the two triangles are \( \triangle TUW \) and \( \triangle WVU \)? Wait, no, the triangles are \( \triangle T UW \) and \( \triangle V W U \). The sides \( TU \) and \( WV \) are equal (tick marks), the angle between \( TU \) and \( UW \) ( \( \angle TUW \)) and the angle between \( WV \) and \( UW \) ( \( \angle WVU \))? Wait, no, the angles at \( U \) and \( W \) are equal (the marked angles), and the side \( UW \) is common. Wait, actually, the two sides with tick marks are \( TU \) and \( WV \), the included angle between them is \( \angle TUW \) and \( \angle WVU \)? No, wait, the common side is \( UW \), and the other sides \( TU = WV \), and the angle between \( TU \) and \( UW \) ( \( \angle TUW \)) is equal to the angle between \( WV \) and \( UW \) ( \( \angle WVU \))? Wait, no, the diagram shows that \( \angle TUW \) and \( \angle WVU \) are equal? Wait, no, the angles at \( U \) and \( W \) are equal (the curved marks), and the sides \( TU = WV \), and the side \( UW \) is common. Wait, actually, the congruence criterion here is SAS (Side - Angle - Side). Let's recall: SAS states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent. Here, \( TU = WV \) (given by tick marks), \( \angle TUW=\angle WVU \) (the marked angles), and \( UW = WU \) (common side). So two sides and the included angle, so SAS.

Answer:

D. SAS