Name two triangles that are congruent by ASA.
Three triangles are shown, triangle P Q R, triangle S T U, and triangle X W V. Side P R, side S T, and side W V are marked congruent. Angle R, angle T, and angle W are marked congruent. Angle P, angle U, and angle V are marked congruent.
On triangle P Q R, segment P R is marked with 1 tick mark, angle P is marked with 1 arc, and angle R is marked with 2 arcs.
On triangle V X W, segment V W is marked with 1 tick mark, angle V is marked with 1 arc, and angle W is marked with 2 arcs.
On triangle U S T, segment S T is marked with 1 tick mark, angle U is marked with 1 arc, and angle T is marked with 2 arcs.
(1 point)
Responses
Triangle P Q R is congruent to Triangle U S T
Image with alt text: Triangle P Q R is congruent to Triangle U S T
Tringle P R Q is congruent to triangle V W X
Image with alt text: Tringle P R Q is congruent to triangle V W X
Triangle T S U is congruent to triangle W V X
Image with alt text: Triangle T S U is congruent to triangle W V X
Triangle R Q P is congruent to triangle X V W
Triangle R Q P is congruent to triangle X V W
Triangle R Q P is congruent to triangle X V W
To determine which triangles are congruent by ASA (Angle-Side-Angle), we need to identify the following:
1. Two triangles with one pair of congruent angles.
2. Sides that are proportional or congruent in length that are not included between the congruent angles.
3. A second pair of congruent angles, where the included side between them is also congruent.
In the given information, the triangles that meet these conditions are:
1. Triangle PQR (angle P, angle R, and side PR) is congruent to Triangle UST (angle U, angle T, and side ST).
2. Triangle PRQ (angle P, angle Q, and side PR) is congruent to Triangle VWX (angle V, angle X, and side VW).
Therefore, the two triangles that are congruent by ASA are Triangle PQR congruent to Triangle UST and Triangle PRQ congruent to Triangle VWX.