Question
Which triangles are congruent by AAS?
Three triangles are shown with markings on sides and angles.Triangle V T U has one tick mark on side T U, one angle mark on angle T, and two angle marks on angle V.
Triangle H F G has two tick marks on side H F, one angle mark on angle F, and two angle marks on angle H.
Triangle C A B has one tick mark on side A B, two tick marks on side C A, one angle mark on angle A, and two angle marks on angle C.
(1 point)
Responses
Triangle V T U and Triangle C A B
Image with alt text: Triangle V T U and Image with alt text: Triangle C A B
Triangle V T U and Triangle H F G
Image with alt text: Triangle V T U and Image with alt text: Triangle H F G
Triangle H F G and Triangle C A B
Image with alt text: Triangle H F G and Image with alt text: Triangle C A B
none of the above
Triangle V T U and Triangle C A B
Triangle V T U and Triangle C A B
To determine which triangles are congruent by Angle-Angle-Side (AAS), we need to look for triangles that have two pairs of congruent angles and a congruent side that is not included between those angles.
In the given information, Triangle V T U has two angle marks on angle V and one angle mark on angle T. Triangle C A B has two angle marks on angle C and one angle mark on angle A.
Therefore, Triangle V T U and Triangle C A B have two pairs of congruent angles. To complete the AAS congruence, we also need to check if they have a congruent side that is not included between those angles. In this case, Triangle V T U has one tick mark on side T U, while Triangle C A B has one tick mark on side A B. Since side T U and side A B are congruent, we can conclude that Triangle V T U and Triangle C A B are congruent by AAS.
Hence, the correct answer is Triangle V T U and Triangle C A B.