Based on the drawing, which can be used to prove Triangle P Q R is congruent to triangle S T V.?
Triangle P Q R is shown with angle R marked with one arc; segment P R has one tick mark; segment Q R has two tick marks. Triangle S T V is shown with angle V marked with one arc; segment S V has one tick mark; segment T V has two tick marks.
(1 point)
Responses
SSS
SSS
SAS
SAS
ASA
ASA
AAS
The correct answer is SAS (Side-Angle-Side).
To prove that Triangle PQR is congruent to Triangle STV based on the given information, we can use the SAS (Side-Angle-Side) congruence criterion.
Explanation:
1. The given information states that segment PR has one tick mark and segment QR has two tick marks, while segment SV has one tick mark and segment TV has two tick marks. This tells us that segments PR and SV are congruent, and segments QR and TV are congruent.
2. The given information also states that angle R has one arc, while angle V has one arc. This means that angle R and angle V are congruent.
By applying the SAS criterion, which requires two pairs of corresponding sides and one pair of corresponding angles to be congruent, we can conclude that Triangle PQR is congruent to Triangle STV.
To prove that Triangle PQR is congruent to Triangle STV, we can use the SAS (Side-Angle-Side) congruence criterion.
First, let's understand what SAS means:
SAS states that if two triangles have two pairs of corresponding sides congruent and the included angles congruent, then the triangles are congruent.
Now, let's analyze the given information in the drawing:
1. We have segment PR with one tick mark, and segment QR with two tick marks. This indicates that these two sides have different lengths.
2. We have segment SV with one tick mark and segment TV with two tick marks. Similarly, this indicates that these two sides have different lengths.
3. Angle R is marked with one arc, and angle V is marked with one arc. This indicates that these angles are congruent.
Based on this information, we have the following:
Side PR is unequal to side SV.
Side QR is unequal to side TV.
Angle R is congruent to angle V.
Since we have two pairs of corresponding sides that are congruent (PR/SV and QR/TV) and one pair of congruent angles (angle R/V), we can conclude that Triangle PQR is congruent to Triangle STV by the SAS congruence criterion.