ΔPQR has vertices P(1, 1), Q(4, 1), and R(1, 5). Triangle STU has vertices S(6, 2), T(9, 2), and U(6, 6). Are these two triangles congruent?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. Yes, by SSS.
By looking at the given coordinates, we can easily compute the side lengths.
For ΔPQR: Horizontal length PQ = 4 – 1 = 3, vertical length PR = 5 – 1 = 4
The longest side QR = √(32 + 42) = 5.
For ΔSTU: Horizontal length ST = 9 – 6 = 3, vertical length SU = 6 – 2 = 4
The longest side TU = √(32 + 42) = 5
All three corresponding sides of both triangles are 3, 4, and 5, so they are equal in length.
Therefore, the correct answer is Yes, by SSS.